(a) Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.
(b) Two air-filled capacitors of capacitances $C_1$ and $C_2$ are connected in parallel with a dc battery. After the capacitors are fully charged, a ...
CBSE CLASS 12 • PHYSICS • CHAPTER 02
Electrostatic Potential and Capacitance
160 distinct questions across 216 board paper set appearances (2022–2026).
(i) The total capacitance of the circuit is : (A) 6 $\mu\text{F}$ (B) 3 $\mu\text{F}$ (C) 9 $\mu\text{F}$ (D) 2 $\mu\text{F}$
The potential difference between point A and B is : (A) 2 V (B) 0.3 V (C) 0.2 V (D) 3 V
(a) An electric iron rated $2\cdot 2\text{ kW}, 220\text{ V}$ is operated at $110\text{ V}$ supply. Find :
(i) its resistance, and
(ii) heat produced by it in $10$ minutes.
OR
(b) A current of $4\cdot 0\text{ A}$ flows through a wire of length $1\text{ m}$ and cross-sectional area $1\cdot 0\text{ mm...
(a) A potential difference $V$ is applied across the ends of a cylindrical conductor of length $l$, area of cross-section $A$ and resistance $R$. It is gradually stretched till its length is tripled. How will (i) the drift speed of electrons in the conductor, and (ii) the resistance of the conductor...
A parallel plate capacitor consists of two conducting plates kept generally parallel to each other at a distance. When the capacitor is charged, the charge resides on the inner surfaces of the plates and an electric field is set up between them. Thus, electrostatic energy is stored in the capacitor....
A charged particle gains a speed of $10^6 \text{ ms}^{-1}$, when accelerated from rest through a potential difference $10\text{ kV}$. It enters a region of magnetic field of $0.4\text{ T}$ such that $\vec{v} \perp \vec{B}$. The radius of circular path described by it is :
(A) $2.5\text{ cm}$
(B) $5\...
A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges $Q$ and $-Q$ with potential difference $V = V_1 - V_2$ between them. The ratio $\frac{Q}{V}$ is a constant, denoted by $C$ and is called the capacitance of the capacitor. It is independe...
(ii) A slab (area $A$ and thickness $d_1$) of a linear dielectric of dielectric constant $K$ is inserted between charged plates (charge density $\sigma$) of a parallel plate capacitor [plate area $A$ and plate separation $d$ ($> d_1$)] and opposite charges with charge density of magnitude $\sigma_p$...
(iii) An electric field $E$ is established between the plates of an air filled parallel plate capacitor, with charges $Q$ and $-Q$. $V$ is the volume of the space enclosed between the plates. The energy stored in the capacitor is :
(A) $\frac{1}{2} \varepsilon_0 E^2$
(B) $\varepsilon_0 Q^2 E$
(C) $\...
A capacitor and an inductor are connected in series across an ac source of voltage of variable frequency. The frequency is increased continuously. The nature of the circuit before and after the resonance will be :
(A) inductive only
(B) capacitive only
(C) capacitive and inductive respectively
(D) i...
A circuit consisting of a capacitor $C$, a resistor of resistance $R$ and an ideal battery of emf $V$, as shown in figure is known as RC series circuit.
As soon as the circuit is completed by closing key $S_1$ (keeping $S_2$ open) charges begin to flow between the capacitor plates and the battery te...
(a) Two wires of the same material and the same radius have their lengths in the ratio $2 : 3$. They are connected in parallel to a battery which supplies a current of $15 \text{ A}$. Find the current through the wires. OR (b) In the circuit three ideal cells of e.m.f. $V, V$ and $2V$ are connected ...
Choose the incorrect statement :
(A) The potential difference (V) between the two terminals of a cell in a closed circuit is always less than its emf ($\varepsilon$), during discharge of the cell.
(B) The internal resistance of a cell decreases with the decrease in temperature of the electrolyte.
(...
(a) (i) A dielectric slab of dielectric constant 'K' and thickness 't' is inserted between plates of a parallel plate capacitor of plate separation d and plate area A. Obtain an expression for its capacitance. (ii) Two capacitors of different capacitances are connected first (1) in series and then (...
The given figure shows a capacitor C and a resistor R connected in series to an ac source. $V_1$ and $V_2$ are voltmeters and A is an ammeter.
Which of the following statements is correct ?
(a) Current in the circuit lags in phase with voltage shown in $V_2$.
(b) The voltage shown in $V_1$ is ahead...
A parallel plate capacitor is an arrangement of two identical metal plates kept parallel, a small distance apart. The capacitance of a capacitor depends on the size and separation of the two plates and also on the dielectric constant of the medium between the plates. Like resistors, capacitors can a...
Find the ratio of the de Broglie wavelengths associated with an alpha particle and a proton, if both
(a) have the same speeds,
(b) have the same kinetic energy,
(c) are accelerated through the same potential difference.
The figure shows the variation of capacitive reactance ($X_C$) of two ideal capacitors of capacitances $C_1$ \& $C_2$ with the reciprocal of angular frequency ($1/\omega$) of ac source. The value of $C_1/C_2$ is
(A) $\frac{1}{2}$
(B) $2$
(C) $\sqrt{3}$
(D) $\frac{1}{\sqrt{3}}$
The value of charge on the plates of the 6 $\mu\text{F}$ capacitor is : (A) 6 $\mu\text{C}$ (B) 4 $\mu\text{C}$ (C) 12 $\mu\text{C}$ (D) 8 $\mu\text{C}$
The wire between two capacitors is cut at point P. The current in the circuit will : (A) increase (B) decrease (C) remain the same (D) first increase then become stable
(a) (i) Explain the following statements giving reason :
(I) An equipotential surface through a point is normal to the electric field at that point.
(II) When a dielectric is placed in an external electric field, the electric field inside the dielectric is less than that outside it.
(III) The potent...
Two parallel plate capacitors X and Y are connected in series to a $6\text{ V}$ battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant $4$.
(a) Calculate the capacitances of X and Y, ...
(b) Two charges of $8\text{ }\mu\text{C}$ and $-4\text{ }\mu\text{C}$ are located at points $(-18\text{ cm}, 0, 0)$ and $(18\text{ cm}, 0, 0)$ respectively.
(i) Calculate the electrostatic potential energy of the system of the two charges.
(ii) The same system of charges is placed in a region where ...
(b) In the given circuit diagram, find the potential difference between points B and D.
The separation between the plates of same area ($L^2$) of a parallel plate air capacitor having capacitance equal to that of this system, will be :
(A) $\frac{d}{K}$
(B) $\frac{2d}{K}$
(C) $\frac{d}{2K}$
(D) $\frac{d}{4K}$
A metal sheet is inserted between the plates of a parallel plate capacitor of capacitance $C$. If the sheet partly occupies the space between the plates, the capacitance :
(A) remains $C$
(B) becomes greater than $C$
(C) becomes less than $C$
(D) becomes zero
Consider a capacitor of capacitance $C$, with plate area $A$ and plate separation $d$, filled with air [Fig. (a)]. The distance between the plates is increased to $2d$ and one of the plates is shifted as shown in Fig. (b). The capacitance of the new system now is :
(A) $\frac{C}{4}$
(B) $\frac{C}{...
32. (a) (i) A parallel plate capacitor with plate area $A$ and plate separation $d$ has a capacitance $C_0$. A slab of dielectric constant $K$ having area $A$ and thickness $\left(\frac{d}{4}\right)$ is inserted in the capacitor, parallel to the plates. Find the new value of its capacitance.
(a) A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current ($I_c$) and the displacement current ($I_d$) has the same value at all points of the circuit. (b) In case (a) above, is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor ? Exp...
A parallel plate capacitor has two parallel plates which are separated by an insulating medium like air, mica, etc. When the plates are connected to the terminals of a battery, they get equal and opposite charges and an electric field is set up in between them. This electric field between the two pl...
The electric field between the plates of a parallel plate capacitor is E. Now the separation between the plates is doubled and simultaneously the applied potential difference between the plates is reduced to half of its initial value. The new value of the electric field between the plates will be:
(...
Electrons drift with speed $v_d$ in a conductor with potential difference $V$ across its ends. If $V$ is reduced to $\left$ \frac{V}{2} \right$$, their drift speed will become :
(A) $\frac{v_d}{2}$
(B) $v_d$
(C) $2 v_d$
(D) $4 v_d$
Two particles A and B of the same mass but having charges $q$ and $4q$ respectively, are accelerated from rest through different potential differences $V_A$ and $V_B$ such that they attain same kinetic energies. The value of $\left(\frac{V_A}{V_B}\right)$ is :
(A) $\frac{1}{4}$ (B) $\frac{1}{2}$ (C)...
(a) (i) Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates. (ii) A charge of 6 $\mu\text{C}$ is given to a hollow metallic sphere of radius 0.2 m. Find the potential at (i) the surface and (ii) the centre of the sphere.
Dielectrics play an important role in design of capacitors. The molecules of a dielectric may be polar or non-polar. When a dielectric slab is placed in an external electric field, opposite charges appear on the two surfaces of the slab perpendicular to electric field. Due to this an electric field ...
In which of the following diagrams is the capacitor 'C' connected correctly to provide smooth output of a half-wave rectifier?
(c) Find the equivalent capacitance between points A and B, if capacitance of each capacitor is C.
In a series LCR circuit, the voltage across the resistor, capacitor and inductor is $10\text{ V}$ each. If the capacitor is short circuited, the voltage across the inductor will be
(A) $10\text{ V}$
(B) $5\sqrt{2}\text{ V}$
(C) $\\frac{5}{\sqrt{2}}\text{ V}$
(D) $10\sqrt{2}\text{ V}$
A parallel plate capacitor of capacitance $C$ has a dielectric slab between its plates. It is charged to a potential difference $V$ by connecting it across a battery. The battery is then disconnected. If the dielectric slab is now withdrawn from the capacitor, how will the following be affected ?
(a...
Figure shows a narrow beam of electrons entering with a velocity of $3 \ imes 10^7 \text{ m/s}$, symmetrically through the space between two parallel horizontal plates $P_1 P_1^{\prime}$ and $P_2 P_2^{\prime}$ kept $2\text{ cm}$ apart.\nIf each plate is $3\text{ cm}$ long, calculate the potential di...
Figure shows a narrow beam of electrons entering with a velocity of $3 \times 10^7$ m/s, symmetrically through the space between two parallel horizontal plates $P_1 P_1^{\prime}$ and $P_2 P_2^{\prime}$ kept $2$ cm apart.
If each plate is $3$ cm long, calculate the potential difference V applied bet...
A $12.0\text{ }\mu\text{F}$ capacitor is charged to a potential difference of $150\text{ V}$. The terminals of the charged capacitor are then connected to those of an uncharged $6.0\text{ }\mu\text{F}$ capacitor. Calculate final potential difference across and charge on, each capacitor.
Figure shows a narrow beam of electrons entering with a velocity of $3 \times 10^7 \text{ m/s}$, symmetrically through the space between two parallel horizontal plates $P_1 P_1^{\prime}$ and $P_2 P_2^{\prime}$ kept $2 \text{ cm}$ apart.
If each plate is $3 \text{ cm}$ long, calculate the potential d...
A parallel plate capacitor of capacitance $C$ is charged to $V$ volt by a battery. After sometime the battery is disconnected and the distance between the plates is doubled. A slab of dielectric constant $k = 1.8$ is then introduced to completely fill the space between the plates. How will the follo...
Find ratio $(\lambda_{ ext{a}}/\lambda_{ ext{p}})$ of the de Broglie wavelength $\lambda_{ ext{a}}$ and $\lambda_{ ext{p}}$ associated respectively with an alpha particle and a proton,\n(i) if they are moving with the same kinetic energy.\n(ii) just after they are accelerated through the same potent...
Find ratio ($\lambda_{\text{a}} / \lambda_{\text{p}}$) of the de Broglie wavelength $\lambda_{\text{a}}$ and $\lambda_{\text{p}}$ associated respectively with an alpha particle and a proton,
(i) if they are moving with the same kinetic energy.
(ii) just after they are accelerated through the same po...
The figure shows the variation of capacitive reactance ($X_C$) of two ideal capacitors of capacitances $C_1$ & $C_2$ with the reciprocal of angular frequency ($1/\omega$) of ac source. The value of $C_1/C_2$ is
(A) $\frac{1}{2}$
(B) $2$
(C) $\sqrt{3}$
(D) $\frac{1}{\sqrt{3}}$
Find ratio ($\lambda_{\alpha} / \lambda_{ ext{p}}$) of the de Broglie wavelength $\lambda_{\alpha}$ and $\lambda_{ ext{p}}$ associated respectively with an alpha particle and a proton,
(i) if they are moving with the same kinetic energy.
(ii) just after they are accelerated through the same potentia...
(a) A particle of charge $q$ and mass $m$ is accelerated through a potential difference $V$. Deduce an expression for the de Broglie wavelength associated with the particle.
(b) Plot a graph for a particle of charge $q$ and mass $m$ showing variation of de Broglie wavelength $\lambda$ with $\frac{1}...
A $50 \text{ } \mu\text{F}$ capacitor, $0.32 \text{ H}$ inductor and $50 \text{ } \Omega$ resistor are connected in series across a $220 \text{ V}$, $50 \text{ Hz}$ ac source. Calculate (i) the impedance of the circuit, and (ii) the current in the circuit.
(a) A proton and an electron are moving with the same velocity. Which one has a greater de Broglie wavelength and why? (b) The de Broglie wavelength associated with an electron when accelerated by a potential difference $V$ is $\lambda$. Find the wavelength of the electron when accelerated by a pote...
(b) (i) Define electric power and give its SI unit. A potential difference V is applied across a resistance R. Find a relation for the power consumed. (ii) A 60 W bulb and a 120 W bulb are connected to a 220 V ac mains (I) first in series, and then (II) is parallel. Which of the bulbs will consume m...
An electron and a proton are accelerated through the same potential difference. Let $\lambda_e$ and $\lambda_p$ be the de Broglie wavelength associated with electron and proton respectively. Then $\lambda_e/\lambda_p$ is (A) $m_e/m_p$ (B) $m_p/m_e$ (C) $\sqrt{\frac{m_e}{m_p}}$ (D) $\sqrt{\frac{m_p}{...
(a) Deduce the relation between the electric field $\vec{E}$ at a point due to a charge Q and (i) the force $\vec{F}$ on a charge q placed at that point. (ii) the potential at that point due to charge Q. (b) Three point charges, q each, are placed at the three vertices of an equilateral triangle of ...
Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. Whe...
OR
The wire between two capacitors is cut at point P. The current in the circuit will :
(A) increase
(B) decrease
(C) remain the same
(D) first increase then become stable
(iv) (a) The value of charge on the plates of the $6 \mu\text{F}$ capacitor is : (A) $6 \mu\text{C}$ (B) $4 \mu\text{C}$ (C) $12 \mu\text{C}$ (D) $8 \mu\text{C}$
33. (a) (i) Explain the following statements giving reason :
(I) An equipotential surface through a point is normal to the electric field at that point.
(II) When a dielectric is placed in an external electric field, the electric field inside the dielectric is less than that outside it.
(III) The po...
What is displacement current ($i_d$) ? Considering the case of charging of a capacitor, show that $i_d = \varepsilon_0 \frac{d\phi_E}{dt}$. What is the value of $i_d$ for a conductor across which a constant voltage is applied ?
What is meant by displacement current ? A capacitor is being charged by a battery. Show that Ampere-Maxwell law justifies continuity and constancy of the current flowing in the circuit.
(a) A diode is connected to $220\text{ V } (\text{rms})$ ac source in series with a capacitor as shown in the diagram.
Find the voltage $(\text{rms})$ across the capacitor.
(a) Briefly explain the process of charging a parallel plate capacitor, when it is connected across a $\text{dc}$ source.
(b) A capacitor, of capacitance $C$, plate area $A$ and plate separation $d$ is charged to $V$ volts by a battery. The energy stored in it is $U$. After some time, the battery is disconnected and a slab of dielectric constant $K$, is inserted to fill the space between the plates of the capacitor. Le...
(a) Two infinitely long thin straight wires $\text{AB}$ and $\text{CD}$ with charge densities $-\frac{12\,\mu\text{C}}{\text{m}}$ and $+\frac{12\,\mu\text{C}}{\text{m}}$ are lying parallel to $\text{y-axis}$ at points $(-1\,\text{m}, 0, 0)$ and $(1\,\text{m}, 0, 0)$ respectively, as shown in the fig...
(a) Find the expression for the induced charge on a surface of a linear dielectric slab (dielectric constant $\text{K}$) inserted between the parallel plates of a charged capacitor fully occupying the intervening region.
(b) Four capacitors, each of capacitance $1\,\mu\text{F}$ are to be connected t...
(a) A diode is connected to $220\text{ V (rms)}$ ac source in series with a capacitor as shown in the diagram.
Find the voltage (rms) across the capacitor.
(b) Find $V_{\text{AB}}$ in the circuit given below.
(a) A diode is connected to $220\text{ V}$ (rms) ac source in series with a capacitor as shown in the diagram.\nFind the voltage (rms) across the capacitor.\n(b) Find $V_{AB}$ in the circuit given below.
The following graph shows the potential difference across the terminals of a cell against its load current.
(IV) In the figure, potential difference between $A$ and $B$ is
(A) Zero
(B) $5 ext{ V}$
(C) $10 ext{ V}$
(D) $15 ext{ V}$
(A) A dielectric slab of thickness $t$, is introduced between the plates of parallel plate capacitor of area $A$ and separation $d$ (where $t<d$). Find an expression for the capacitance with the dielectric slab.
(B) A copper sphere of capacitor $C$ is dropped in ocean. Will the capacitance of the sp...
For VI Candidates
(C) A capacitor is connected across potential difference V and is then separation between plates 'd' is increase using insulating stick. Will the energy stored in capacitor increase or decrease? Justify
(A) If a charge of $1\text{ \mu C}$ is placed at the origin and another charge of $3\text{ \mu C}$ placed at the point $(20\text{m}, 0\text{m}, 0\text{m})$ in an external uniform electric field of $40\text{V/m }\hat{i}$ with the electric potential at origin to be zero. Find the electrical potential ...
A $50\text{ pF}$ capacitor is charged by a $100\text{ V}$ battery. The battery is disconnected and the capacitor is connected to another uncharged $50\text{ pF}$ capacitor. Find the energy stored in the combination.
A current of $4\cdot0\text{ A}$ passes through a wire, when a potential difference of $6\cdot0\text{ V}$ is applied across it. The length of the wire and its area of cross-section respectively are $4\text{ m}$ and $8\times 10^{-6}\text{ m}^2$. Find the electrical conductivity of the material of the ...
(a) (i) When a potential difference is applied across the ends of a conductor, the free electrons must accelerate along the length of the conductor. But they acquire a steady drift speed. Explain why.
A parallel plate capacitor of capacitance $C$ is connected to a battery. Explain how the plates of the capacitor acquire equal and opposite charges. Hence obtain expression for the energy stored in the capacitor.
(ii) A parallel plate capacitor has $+4\cdot 0 ext{ }\mu ext{C}$ and $-4\cdot 0 ext{ }\mu ext{C}$ charges on its plates. Find the area of each plate so that an electric field of $1600 ext{ V/mm}$ is produced between the plates.
The capacitance of the system between A and B will be :
(A) $\frac{\varepsilon_0 KL^2}{d}$
(B) $\frac{\varepsilon_0 KL^2}{2d}$
(C) $\frac{2\varepsilon_0 KL^2}{d}$
(D) $\frac{2\varepsilon_0 Kd}{L^2}$
OR
If the source of potential difference applied between A and B is removed, and then A and B are connected by a conducting wire, the net charge on the system will be :
(A) $\frac{\varepsilon_0 VKL^2}{4d}$
(B) $\frac{\varepsilon_0 VKL^2}{2d}$
(C) $\frac{\varepsilon_0 VKL^2}{d}$
(D) Zero
The electric field in space between the plates of a parallel plate capacitor (each of area $2.5 \times 10^{-3}\text{ m}^2$) is changing at the rate of $4 \times 10^6\text{ Vm}^{-1}\text{s}^{-1}$. The displacement current between the plates of the capacitor is :
(A) $1.8 \times 10^{-5}\text{ A}$
(B) ...
If the source of potential difference applied between A and B is removed, and then A and B are connected by a conducting wire, the net charge on the system will be :
(A) $\frac{\varepsilon_0 \text{VKL}^2}{4\text{d}}$
(B) $\frac{\varepsilon_0 \text{VKL}^2}{2\text{d}}$
(C) $\frac{\varepsilon_0 \tex...
(iv) (a) The separation between the plates of same area ($L^2$) of a parallel plate air capacitor having capacitance equal to that of this system, will be :
(A) $\frac{d}{K}$
(B) $\frac{2d}{K}$
(C) $\frac{d}{2K}$
(D) $\frac{d}{4K}$
OR
(b) If the source of potential difference applied between A and...
A parallel plate capacitor has plate area $\text{A}$ and plate separation $\text{d}$. Half of the space between the plates is filled with a material of dielectric constant $\text{K}$ in two ways as shown in the figure.
Find the values of the capacitance of the capacitors in the two cases.
The effective capacitance of the network between points A and B shown in the figure is :
(A) $\frac{4}{3} \text{ } \mu\text{F}$
(B) $2 \text{ } \mu\text{F}$
(C) $\frac{3}{2} \text{ } \mu\text{F}$
(D) $6 \text{ } \mu\text{F}$
A capacitor of plate area A and plate separation d is charged by a battery to voltage V. The battery is disconnected and plates are slowly pulled apart till the separation becomes $2\text{d}$. Find the value of :
(a) potential difference between the plates,
(b) electric field between the plates,
(c)...
A capacitor of capacitance $C$ has reactance $X$ in an ac circuit. If the capacitance and the frequency of the applied voltage are doubled, the new reactance will become :
(A) $4X$
(B) $2X$
(C) $\frac{X}{2}$
(D) $\frac{X}{4}$
(a) "There is a limit to the amount of charge that can be stored on a given capacitor." Explain.
(b) A capacitor is charged by a battery to a potential difference $V$. It is disconnected from the battery and connected across another identical uncharged capacitor. Calculate the ratio of total energy ...
(iv) (a) Three capacitors A, B and M, each of capacitance $C$ are connected to a capacitor N of capacitance $2C$ and a battery as shown in the figure. If the charges on A and N are $Q$ and $Q'$ respectively, then $\frac{Q'}{Q}$ is :
(A) $\frac{1}{6}$
(B) $\frac{1}{3}$
(C) $3$
(D) $6$
(b) A slab (area A and thickness $\frac{\text{d}}{2}$) of dielectric constant K is inserted in a parallel plate capacitor of plate area A and plate separation d. If C and $C_0$ are the capacitances of the capacitors with and without the dielectric, then $\frac{\text{C}}{\text{C}_0}$ is :
(A) $\frac{...
Three capacitors A, B and M, each of capacitance C are connected to a capacitor N of capacitance $2\text{C}$ and a battery as shown in the figure. If the charges on A and N are Q and $Q'$ respectively, then $\frac{Q'}{Q}$ is :
(A) $\frac{1}{6}$
(B) $\frac{1}{3}$
(C) $3$
(D) $6$
OR
(b) A slab (...
The ratio of potential difference across AB in the circuit shown for the case (i) when switch S is closed and (ii) when S is open is :
(A) $\frac{1}{4}$
(B) $\frac{1}{2}$
(C) $1$
(D) $2$
An alpha particle and a deuterium ion are accelerated through the same potential difference. These are then directed towards a target nucleus to make head-on collision. It is observed that their distance of closest approach is the same. Justify it theoretically.
Like resistors, capacitors can also be arranged in series or in parallel or in a combination of series and parallel.
Three capacitors A, B and M, each of capacitance C are connected to a capacitor N of capacitance 2C and a battery as shown in the figure. If the charges on A and N are Q and $Q'$ res...
OR
A slab (area A and thickness $\frac{\text{d}}{2}$) of dielectric constant K is inserted in a parallel plate capacitor of plate area A and plate separation d. If C and $C_0$ are the capacitances of the capacitors with and without the dielectric, then $\frac{C}{C_0}$ is :
(A) $\frac{K + 1}{2K}$
...
Two horizontal plates, separated by $1\text{ cm}$, are arranged one above the other. A particle of mass $5\text{ mg}$ and charge $2\text{ nC}$ is released in air between the plates. The potential difference that should be applied to the plates so that the particle remains suspended between them, is ...
(a) (i) A parallel plate capacitor with plate area $A$ and plate separation $d$ has a capacitance $C_0$. A slab of dielectric constant $K$ having area $A$ and thickness $\left(\frac{d}{4}\right)$ is inserted in the capacitor, parallel to the plates. Find the new value of its capacitance.
(ii) You ar...
In the circuit shown, the charge on the left plate of $20\text{ }\mu\text{F}$ capacitor is $-50\text{ }\mu\text{C}$. The charge on the right plate of the $12\text{ }\mu\text{F}$ capacitor is :
(A) $20\text{ }\mu\text{C}$
(B) $-20\text{ }\mu\text{C}$
(C) $30\text{ }\mu\text{C}$
(D) $-30\text{ }\mu\t...
(ii) You are provided with a large number of $1\text{ }\mu\text{F}$ identical capacitors and a power supply of $1200\text{ V}$. The dielectric medium used in each capacitor can withstand up to $200\text{ V}$ only. Find the minimum number of capacitors and their arrangement, required to build a capac...
Ten capacitors, each of capacitance $1\text{ }\mu\text{F}$, are connected in parallel to a source of $100\text{ V}$. The total energy stored in the system is equal to :
(A) $10^{-2}\text{ J}$
(B) $10^{-3}\text{ J}$
(C) $0.5 \times 10^{-3}\text{ J}$
(D) $5.0 \times 10^{-2}\text{ J}$
The reactance of a capacitor of capacitance $C$ connected to an ac source of frequency $\omega$ is 'X'. If the capacitance of the capacitor is doubled and the frequency of the source is tripled, the reactance will become :
(A) $\frac{X}{6}$
(B) $6X$
(C) $\frac{2}{3}X$
(D) $\frac{3}{2}X$
An inductor, a capacitor and a resistor are connected in series with an ac source $v = v_m \sin \omega t$. Derive an expression for the average power dissipated in the circuit. Also obtain the expression for the resonant frequency of the circuit.
A battery of emf E and internal resistance r is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of E and r.
(a) A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current $(\text{I}_\text{c})$ and the displacement current $(\text{I}_\text{d})$ has the same value at all points of the circuit. (b) In case (a) above, is Kirchhoff's first rule (junction rule) valid at each ...
(i) The final charge on the capacitor, when key $S_1$ is closed and $S_2$ is open, is
(A) $5\text{ }\mu\text{C}$
(B) $5\text{ mC}$
(C) $25\text{ mC}$
(D) $0.1\text{ C}$
(ii) For sufficient time the key $S_1$ is closed and $S_2$ is open. Now key $S_2$ is closed and $S_1$ is open. What is the final ch...
(a) (i) Two point charges $5 \mu\text{C}$ and $-1 \mu\text{C}$ are placed at points $(-3 \text{ cm}, 0, 0)$ and $(3 \text{ cm}, 0, 0)$ respectively. An external electric field $\vec{E} = \frac{A}{r^2} \hat{r}$ where $A = 3 \times 10^5 \text{ Vm}$ is switched on in the region. Calculate the change in...
In the figure curved lines represent equipotential surfaces. A charge Q is moved along different paths A, B, C and D. The work done on the charge will be maximum along the path
(A) A
(B) B
(C) C
(D) D
(a) (i) Two point charges 5 $\mu$C and -1 $\mu$C are placed at points (-3 cm, 0, 0) and (3 cm, 0, 0) respectively. An external electric field $\vec{E} = \frac{A}{r^2} \hat{r}$ where A = 3 $\times$ $10^5$ Vm is switched on in the region. Calculate the change in electrostatic energy of the system due ...
n identical cells, each of e.m.f. E and internal resistance r, are connected in series. Later on it was found out that two cells 'X' and 'Y' are connected in reverse polarities. Calculate the potential difference across the cell 'X'.
(a) (i) Two point charges $5\text{ }\mu\text{C}$ and $-1\text{ }\mu\text{C}$ are placed at points $(-3\text{ cm}, 0, 0)$ and $(3\text{ cm}, 0, 0)$ respectively. An external electric field $\vec{E} = \frac{A}{r^2}\hat{r}$ where $A = 3 \times 10^5\text{ Vm}$ is switched on in the region. Calculate the...
Question numbers 29 and 30 are case study based questions. Read the following paragraphs and answer the questions that follow.
A parallel plate capacitor has two parallel plates which are separated by an insulating medium like air, mica, etc. When the plates are connected to the terminals of a batte...
A material of dielectric constant $K$ is filled in a parallel plate capacitor of capacitance $C$. The new value of its capacitance becomes
(A) $C$
(B) $\frac{C}{K}$
(C) $CK$
(D) $C\left$1 + \frac{1}{K}\right$$
Question Numbers 29 and 30 are Case-Study based questions. Read the following paragraphs and answer the questions that follow :
A power supply is connected across the two plates of a capacitor. Consequently, one plate becomes positively charged and the other plate becomes negatively charged. Thus a ...
(iii) The potential difference between the two plates of a capacitor is V. An electron of mass m and charge -e is released from rest near the negative plate. The maximum speed gained by the electron is
(A) 2eVm
(B) $\sqrt{\frac{em}{2V}}$
(C) $\sqrt{\frac{2eV}{m}}$
(D) $\sqrt{\frac{2me}{V}}$
(a) The electric field between two parallel plates of a charged capacitor is $200\text{ V/m}$. The plates are $5\text{ mm}$ apart. The potential difference between the two plates is
(A) $20\text{ V}$
(B) $10\text{ V}$
(C) $5.0\text{ V}$
(D) $1.0\text{ V}$
(b) (A) Differentiate between the electrostatic force and the gravitational force between two charged particles.
(B) A potential difference of 480 V is applied between two large horizontal plates, kept one above the other, 3.0 cm apart. A charged particle of mass 4 × 10^{-11} kg, when released at re...
Two batteries of emfs $6\text{ V}$ and $3\text{ V}$ and internal resistances $0\cdot8\text{ }\Omega$ and $0\cdot2\text{ }\Omega$ respectively are connected in series to an external resistance $R$, as shown in figure. Find the value of $R$ so that the potential difference across the $6\text{ V}$ batt...
(a) (i) A resistor and a capacitor are connected in series to an ac source $v = v_m \sin \omega t$. Derive an expression for the impedance of the circuit.
(ii) When does an inductor act as a conductor in a circuit ? Give reason for it.
Two charged particles, P and Q, each having charge $q$ but of masses $m_1$ and $m_2$, are accelerated through the same potential difference $V$. They enter a region of magnetic field $\vec{B}$ $$\perp \vec{v}$$ and describe the circular paths of radii $a$ and $b$ respectively. Then $(\frac{m_1}{m_2}...
An air-filled parallel plate capacitor with plate separation $1\text{ mm}$ has a capacitance of $20\text{ pF}$. It is charged to $4\cdot0\text{ }\mu\text{C}$. Calculate the amount of work done to pull its plates to a separation of $5\text{ mm}$. Assume the charge on the plates remains the same.
A capacitor consists of two parallel plates, with an area of cross-section of $0.001 \text{ m}^2$, separated by a distance of $0.0001 \text{ m}$. If the voltage across the plates varies at the rate of $10^8 \text{ V/s}$, then the value of displacement current through the capacitor is (A) $8.85 \time...
In a series LCR circuit, the voltage across the resistance, capacitance and inductance is $10 \text{ V}$ each. If the capacitance is short circuited the voltage across the inductance will be (A) $10 \text{ V}$ (B) $10\sqrt{2} \text{ V}$ (C) $10/\sqrt{2} \text{ V}$ (D) $20 \text{ V}$
Find the expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d when (I) a dielectric slab of thickness t and (II) a metallic slab of thickness t, where ($t < d$) are introduced one by one between the plates of the capacitor. In which case would the capac...
OR
Potential difference across a cell in the open circuit is $6\text{ V}$. It becomes $4\text{ V}$ when a current of $2\text{ A}$ is drawn from it. The internal resistance of the cell is :
(A) $1.0\text{ }\Omega$
(B) $1.5\text{ }\Omega$
(C) $2.0\text{ }\Omega$
(D) $2.5\text{ }\Omega$
Potential difference across a cell in the open circuit is 6 V. It becomes 4 V when a current of 2 A is drawn from it. The internal resistance of the cell is :
(A) 1.0 $\Omega$
(B) 1.5 $\Omega$
(C) 2.0 $\Omega$
(D) 2.5 $\Omega$
When the terminals of a cell are connected to a conductor of resistance R, an electric current flows through the circuit. The electrolyte of the cell also offers some resistance in the path of the current, like the conductor. This resistance offered by the electrolyte is called internal resistance o...
Potential difference across a cell in the open circuit is $6\text{ V}$. It becomes $4\text{ V}$ when a current of $2\text{ A}$ is drawn from it. The internal resistance of the cell is : (A) $1.0\text{ }\Omega$ (B) $1.5\text{ }\Omega$ (C) $2.0\text{ }\Omega$ (D) $2.5\text{ }\Omega$
Three points charges $+q$, $-4q$ and $+2q$ are kept at the vertices of an equilateral triangle of side 'a'. The electrostatic potential energy of this system of charges is :
(A) $-\frac{1}{4\pi \varepsilon_0} \left$ \frac{q^2}{a^2} \right$$
(B) $+\frac{1}{4\pi \varepsilon_0} \left$ \frac{8q^2}{a^2} ...
The ratio of the de Broglie wavelengths associated with an electron of mass m and of proton of mass M when both are accelerated through a potential difference V is :
(A) $\left$ \frac{M}{m} \right$^{3/2}$
(B) $\frac{m}{M}$
(C) $\sqrt{\frac{M}{m}}$
(D) $\sqrt{\frac{m}{M}}$
Assertion (A) : At a very high frequency, a capacitor can behave as a conductor. Reason (R) : The capacitance of a capacitor depends only on its geometrical configuration and nature of dielectric used.
(a) Define mobility of free electrons in a conductor. How does the mobility of electrons in a metal change when :
(i) temperature of the conductor is decreased at constant potential difference ?
(ii) applied potential difference is doubled at a constant temperature ?
OR
(b) Obtain an expression fo...
Explain the polarization of a dielectric medium filled inside a charged capacitor. How does the capacity of a capacitor increase due to filling ? What is dielectric constant of a dielectric ?
Which of the following statements is not true for equipotential surfaces ?
(A) Potentials at two equipotential surfaces are different.
(B) No work is done in moving a charge on an equipotential surface.
(C) Equipotential surfaces always enclose some volume.
(D) Two equipotential surfaces do not inte...
A and B are two equipotential surfaces around a point charge Q. Surface A is closer to the charge than surface B. If a test charge is released between them, it will :
(A) remain stationary
(B) move from A to B
(C) move from B to A
(D) move around Q in a circular path between the equipotential surfac...
(i) Obtain an expression for the capacitance of a parallel plate capacitor.
(ii) Two identical plates, each of area A having surface charge densities $+\sigma$ and $-\sigma$, respectively, are separated by a distance d in air and a dielectric of dielectric constant K is filled between them. Write th...
A parallel plate capacitor is charged by a battery. The battery is then disconnected and the plates of the charged capacitor are then moved farther apart. In the process :
(A) the charge on the capacitor increases.
(B) the potential difference across the plates decreases.
(C) the capacitance of the ...
The capacitance of a parallel plate capacitor is $10\,\mu\text{F}$ when the distance between its plates is 8 cm. If the distance between the plates is halved, the capacitance will become : (A) $10\,\mu\text{F}$ (B) $15\,\mu\text{F}$ (C) $20\,\mu\text{F}$ (D) $40\,\mu\text{F}$
A capacitor of $5 \text{ } \mu\text{F}$ is connected to an ac source of $200 \text{ V}$, $\frac{1000}{\pi} \text{ Hz}$ through a resistor of $100 \text{ } \Omega$. The phase difference between the voltage (V) applied and current (I) is:
(A) $120^\circ$ (B) $90^\circ$ (C) $60^\circ$ (D) $45^\circ$
An ideal resistor R, an ideal inductor L and an ideal capacitor C are connected, one by one, across the same source of ac voltage $v = v_0 \sin \omega t$. It is observed that the same current I flows in each case. (a) What will be the instantaneous value of current that will flow through their serie...
Consider a group of charges $q_1, q_2, q_3 \dots$ such that $\Sigma q \neq 0$. Then equipotentials at a large distance, due to this group are approximately : (A) Plane (B) Spherical surface (C) Paraboloidal surface (D) Ellipsoidal surface
(i) Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates. (ii) A charge of $6 \text{ } \mu\text{C}$ is given to a hollow metallic sphere of radius $0.2 \text{ m}$. Find the potential at (i) the surface and (ii) the centre of the sphere.
The plates $P_1$ and $P_2$ of a $2\;\mu\text{F}$ capacitor are at potentials $25\;\text{V}$ and $-25\;\text{V}$ respectively. The charge on plate $P_1$ will be :
(A) $0.02\;\text{mC}$
(B) $0.1\;\text{mC}$
(C) $0.1\;\mu\text{C}$
(D) $1\;\mu\text{C}$
An ac source $V = 282 \sin(100 \ t)$ volt is connected across a $1 \ \mu\text{F}$ capacitor. The rms value of current in the circuit will be (take $\sqrt{2} = 1.41$)
(A) $10 \ \text{mA}$
(B) $20 \ \text{mA}$
(C) $40 \ \text{mA}$
(D) $80 \ \text{mA}$
What is meant by displacement current ? How is this current different from the conduction current ? A capacitor is being charged by a source of emf. Justify the continuity of current in the circuit.
An air-filled capacitor with plate area A and plate separation d has capacitance $C_0$. A slab of dielectric constant K, area A and thickness $\left(\frac{d}{5}\right)$ is inserted between the plates. The capacitance of the capacitor will become
(A) $\left[\frac{4K}{5K+1}\right] C_0$
(B) $\left[\fra...
Two capacitors of capacitances $2 C_0$ and $6 C_0$ are first connected in series and then in parallel across the same battery. The ratio of energies stored in series combination to that in parallel is
(A) $\frac{1}{4}$
(B) $\frac{1}{6}$
(C) $\frac{2}{15}$
(D) $\frac{3}{16}$
(iv) (a) An air-filled capacitor with plate area $A$ and plate separation $d$ has capacitance $C_0$. A slab of dielectric constant $K$, area $A$ and thickness $\left(\frac{d}{5}\right)$ is inserted between the plates. The capacitance of the capacitor will become
(A) $\left[\frac{4K}{5K+1}\right]C_0$...
OR
(iv) (b) Two capacitors of capacitances $2 C_0$ and $6 C_0$ are first connected in series and then in parallel across the same battery. The ratio of energies stored in series combination to that in parallel is
(A) $\frac{1}{4}$
(B) $\frac{1}{6}$
(C) $\frac{2}{15}$
(D) $\frac{3}{16}$
A potential difference of $1.0 \text{ V}$ is applied across a conductor of length $5.0 \text{ m}$ and area of cross-section $1.0 \text{ mm}^2$. When current of $4.25 \text{ A}$ is passed through the conductor, calculate
(i) the drift speed and (ii) relaxation time, of electrons. (Given number densit...
A bulb and an inductor of reactance $X_L$ are connected in series with an ac source. How will the brightness of the bulb change when :
(a) an iron rod is inserted in the inductor ?
(b) number of turns in the inductor is decreased ?
(c) a capacitor of capacitive reactance $X_C (= X_L)$ is connected i...
(a) (i) A capacitor of capacitance C is charged to a potential difference V by a battery. The battery is disconnected and the separation between the plates is halved. How will the following quantities be affected? (1) Capacitance of the capacitor (2) Electric field between the plates (3) Energy stor...
A wire of uniform cross-section and resistance 4 ohm is bent in the shape of square ABCD. Point A is connected to a point P on DC by a wire AP of resistance 1 ohm. When a potential difference is applied between A and C, the points B and P are seen to be at the same potential. What is the resistance ...
OR
Two identical $PN$ junctions can be connected in series by three different methods as shown in the figure. If the potential difference in the junctions is the same, then the correct connections will be
(a) in the circuits (1) and (2)
(b) in the circuits (2) and (3)
(c) in the circuits (1) and (3)...
i. Derive an expression for the capacitance of a parallel plate capacitor with air present between the two plates.
ii. Obtain the equivalent capacitance of the network shown in figure. For a $300\text{ V}$ supply, determine the charge on each capacitor.
OR
i. A dielectric slab of thickness 't' is ...
The terminal potential difference of a cell is $19\text{ V}$ when a current of $1.0\text{ A}$ flows in the circuit. It reduces to $17\text{ V}$ when the current supplied by the cell is $3.0\text{ A}$. Find the emf and internal resistance of the cell.
In a series LCR circuit, the capacitance is changed from C to C/4. For the resonant frequency to remain unchanged, the inductance should be changed from L to nL, where n is :
(a) $\frac{1}{2}$
(b) 2
(c) 4
(d) $\frac{1}{4}$
The figure shows a capacitor C, a variable resistor R and a bulb connected in series to the ac source of frequency ($\nu$). The bulb glows with some brightness. How will the glow of the bulb be affected, if the (a) separation between the plates of the capacitor is doubled, keeping resistance R and f...
In which of the following diagrams is the capacitor '$C$' connected correctly to provide smooth output of a half-wave rectifier ?
(a) A circuit diagram showing an AC source in series with a capacitor and a diode, connected across a resistor.
(b) A circuit diagram showing an AC source in parallel w...
(b) (i) How will the capacitance of a parallel plate capacitor change if :
(1) the plates area is doubled ?
(2) the separation between the plates is doubled ?
(ii) The effective capacitance of three capacitors of the same capacitance connected in series is $1\text{ }\mu\text{F}$. Find the :
(1) effe...
(a) Draw equipotential surfaces for (i) an electric dipole and (ii) two identical positive charges placed near each other. (b) In a parallel plate capacitor with air between the plates, each plate has an area of $6 \times 10^{-3} \text{m}^2$ and the separation between the plates is 3 mm. (i) Calcula...