What is the order of magnitude of drift velocity of electrons in a conductor? Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.
CBSE CLASS 12 • PHYSICS • CHAPTER 03
Current Electricity
133 distinct questions across 182 board paper set appearances (2022–2026).
(a) In the given figure, a steady current I flows through the circuit when points A and C are connected by a wire of negligible resistance. Find the potential difference between points B and C. (Figure shows points A, B, and C with $E_1=6\text{ V}$, $1\text{ }\Omega$ and $E_2=4\text{ V}$, $3\text{ }...
Assertion (A): The work done, in taking a unit charge around a closed loop of an electric circuit involving cells and resistors in the loop, is zero. Reason (R): The potential at a point depends on the location of the point in the loop. After completing one round, the charge comes back to the point ...
Five resistors are joined as shown in the figure. Between the points A and B, a battery of $6\text{ V}$ is connected. How much current is flowing in arm FC ?
(A) $2\cdot0\text{ A}$
(B) $1\cdot5\text{ A}$
(C) $1\cdot0\text{ A}$
(D) $0\cdot5\text{ A}$
(a) (i) Derive an expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time.
(ii) The figure shows the plot of current through a cross-section of wire over two different time intervals. Compare the charges ($Q_1$ and $Q_2$) that pass through the c...
Four resistors, each of resistance $R$ and a key $K$ are connected as shown in the figure. The equivalent resistance between points A and B when key $K$ is open, will be :
(A) $4R$
(B) $\infty$
(C) $\frac{R}{4}$
(D) $\frac{4R}{3}$
(a) (i) Three batteries $E_1$, $E_2$ and $E_3$ of emfs and internal resistances ($4\text{ V}$, $2\text{ }\Omega$), ($2\text{ V}$, $4\text{ }\Omega$) and ($6\text{ V}$, $2\text{ }\Omega$) respectively are connected as shown in the figure. Find the values of the currents passing through batteries $E_1...
An ac source is connected to a resistor and an inductor in series. The voltage across the resistor and inductor are $8\text{ V}$ and $6\text{ V}$ respectively. The voltage of the source is :
(A) $10\text{ V}$
(B) $12\text{ V}$
(C) $14\text{ V}$
(D) $16\text{ V}$
In a metallic conductor, an electron, moving due to thermal motion, suffers collisions with the heavy fixed ions but after collision, it will emerge out with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero. When an electric field is appl...
Consider the contribution of the following two factors I and II in resistivity of a metal :
I. Relaxation time of electrons
II. Number of electrons per unit volume
The resistivity of a metal increases with increase in its temperature because :
(A) I decreases and II increases.
(B) I increases a...
The figure shows a network of resistors connected across a battery. Find the current supplied by the battery of emf $5\text{ V}$ and internal resistance $\frac{2}{3}\text{ }\Omega$.
Two cells of emfs $2.0\text{ V}$ and $6.0\text{ V}$ and internal resistances $0.1\text{ }\Omega$ and $0.4\text{ }\Omega$ respectively, are connected in parallel. The equivalent emf of the combination will be :
(A) $2.0\text{ V}$
(B) $2.8\text{ V}$
(C) $6.0\text{ V}$
(D) $8.0\text{ V}$
Assertion (A) : The current density ($\vec{J}$) at a point in a conducting wire is in the direction of electric field ($\vec{E}$) at that point.
Reason (R) : A conducting wire obeys Ohm's law.
(a) What is meant by 'relaxation time' of free electrons in a conductor? Show that the resistance of a conductor can be expressed by $R = \frac{ml}{ne^2\tau A}$, where symbols have their usual meanings. OR (b) Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flow...
Assertion (A) : When electrons drift in a conductor, it does not mean that all free electrons in the conductor are moving in the same direction.
Reason (R) : The drift velocity is superposed over large random velocities of electrons.
Assertion (A) : The temperature coefficient of resistance is positive for metals and negative for semi-conductors.
Reason (R) : The charge carriers in metals are negatively charged whereas in semiconductors they are positively charged.
(a) Two cells of emf $E_1$ and $E_2$ with internal resistances $r_1$ and $r_2$ respectively, are connected in parallel by connecting their positive terminals together and negative terminals together. Deduce an expression for equivalent emf and equivalent internal resistance of the combination.
(b) A...
An ac voltage $V_i = 12 \sin $100 \pi t$ \text{ V}$ is applied between points A and B in a network of two ideal diodes and three resistors as shown in figure. During the positive half-cycle of the input voltage $V_i$ supplied to the network.
(a) Identify which of the two diodes will conduct and why ...
(a) Explain the statement : "Current is a scalar although we represent current with an arrow".
(b) Use Kirchhoff's rules to find the current through $3\text{ }\Omega$ resistor in the circuit shown in the figure :
[Circuit diagram showing nodes A, B, C, D, E, F, with a $3\text{ V}$ battery and $4\tex...
(a) Establish the relation between drift velocity of electrons ($v_d$) and electric current (I) in a conductor. (b) How is $v_d$ affected when the length of the conductor is doubled, keeping the voltage applied across the conductor constant?
Assertion (A): In a Wheatstone bridge circuit, if we interchange the position of the cell and the galvanometer, the balance condition $\frac{\text{P}}{\text{Q}} = \frac{\text{R}}{\text{S}}$ remains unchanged. Reason (R): $\frac{\text{P}}{\text{Q}} = \frac{\text{R}}{\text{S}} \Rightarrow \frac{\text{...
Two cells of emfs $12\text{ V}$ and $6\text{ V}$ are connected in parallel as shown in the figure. Their internal resistances are $1\text{ }\Omega$ and $0\cdot5\text{ }\Omega$ respectively. Calculate the emf and internal resistance of the equivalent cell between points A and B.
If resistor X were made of manganin and readings for V and I are taken without switching off the circuit, the graph between V and I will be as :
(A)
(B)
(C)
(D)
OR
(b) (i) Answer the following giving reason :
(I) The electron drift speed is estimated to be only a few $\text{mm/s}$ for currents in the range of a few amperes. How, then, is the current established almost the instant a circuit is closed ?
(II) A low voltage supply from which one needs high cur...
OR
(a) A cell of emf $E$ and internal resistance $r$ is connected across a resistor of variable resistance $R$. Draw a plot showing the variation of (i) the current ($I$) in the circuit with $R$, and (ii) the terminal potential difference of the cell with $R$.
(a) In the given figure, three identical bulbs P, Q and S are connected to a battery.
(i) Compare the brightness of bulbs P and Q with that of bulb S when key K is closed.
(ii) Compare the brightness of the bulbs S and Q when the key K is opened.
Justify your answer in both cases.
OR
(b) Two cel...
If $R_s$ and $R_p$ are the equivalent resistances of $n$ resistors, each of value $R$, in series and parallel combinations respectively, then the value of $(R_s - R_p)$ is :
(A) $\left(\frac{n^2 - 1}{n^2}\right)R$
(B) $\left(\frac{n^2 + 1}{n^2 - 1}\right)R$
(C) $\left(\frac{n^2 - 1}{n}\right)R$
(D)...
The temperature coefficient of resistance of nichrome is $1\cdot70 \times 10^{-4} \text{ }^\circ\text{C}^{-1}$. In order to increase resistance of a nichrome wire by $8\cdot5%$, the temperature of the wire should be increased by :
(A) $250^\circ\text{C}$
(B) $500^\circ\text{C}$
(C) $850^\circ\text{C...
(a) Define ‘current density’. Is it a scalar or a vector ? An electric field $\vec{E}$ is maintained in a metallic conductor. If $n$ be the number of electrons (mass $m$, charge $-e$) per unit volume in the conductor and $\tau$ its relaxation time, show that the current density $\vec{j} = \alpha \ve...
(a) Two batteries of emf's $3\text{V}$ & $6\text{V}$ and internal resistances $0.2\,\Omega$ & $0.4\,\Omega$ are connected in parallel. This combination is connected to a $4\,\Omega$ resistor. Find : (i) the equivalent emf of the combination (ii) the equivalent internal resistance of the combination ...
Five identical cells, each of emf $2\text{ V}$ and internal resistance $0.1\text{ }\Omega$ are connected in parallel. This combination in turn is connected to an external resistor of $9.98\text{ }\Omega$. The current flowing through the resistor is :
(A) $0.05\text{ A}$
(B) $0.1\text{ A}$
(C) $0....
(b) (i) State Kirchhoff's rules. Use them to obtain the condition of balance for a Wheatstone Bridge.
(ii) Use Kirchhoff's rule to determine the currents flowing through the branches $ ext{MN}$, $ ext{TO}$ and $ ext{SP}$ in the circuit shown in the figure.
(a) (i) Derive the relation between the current and the drift velocity of free electrons in a conductor. Briefly explain the variation of resistance of a conductor with rise in temperature.
(ii) An ammeter, together with an unknown resistance in series is connected across two identical batteries, ea...
An ac voltage $V_i = 12 \sin $100 \pi t$\text{ V}$ is applied between points A and B in a network of two ideal diodes and three resistors as shown in figure.\nDuring the positive half-cycle of the input voltage $V_i$ supplied to the network.\n(a) Identify which of the two diodes will conduct and why...
A resistor and an inductor of negligible resistance are connected in series to a $20\text{ V}$ ac source. If the voltage across the resistor is $12\text{ V}$, the voltage across the inductor will be
(A) $6\text{ V}$
(B) $8\text{ V}$
(C) $10\text{ V}$
(D) $16\text{ V}$
A heating element using nichrome is connected to a $220\text{ V}$ supply. Initially it draws a current of $2.9\text{ A}$. After some time, the current attains a steady value of $2.5\text{ A}$. Find the steady temperature of the heating element if the room temperature is $27\text{ }^\circ\text{C}$. T...
(a) Explain the statement : "Current is a scalar although we represent current with an arrow".
(b) Use Kirchhoff's rules to find the current through $3 ext{ }\Omega$ resistor in the circuit shown in the figure :
Calculate the temperature at which the resistance of a conductor becomes $20%$ more than its resistance at $27\text{ }^\circ\text{C}$. The value of the temperature coefficient of resistance of the material of conductor is $2.0 \times 10^{-4}\text{ }^\circ\text{C}^{-1}$.
(a) Why manganin is used in wire-wound standard resistors ? Calculate the temperature at which the resistance of a wire increases by $25%$ of its resistance at room temperature $27.5 ext{ }^\circ ext{C}$ ? The temperature coefficient of resistance of the material of the wire is $0.004 ext{ }^\circ e...
The resistance of a metal wire at $0^{\circ}\text{C}$ is $5\cdot00\ \Omega$ and is $5\cdot25\ \Omega$ at $100^{\circ}\text{C}$. Calculate the temperature coefficient of resistance of the metal.
(a) (i) Derive the expression for the current density (j) in a current-carrying conductor, in terms of the drift velocity $(v_d)$, the number of free electrons per unit volume (n) and the electrons charge (e).
(ii) Calculate the relaxation time for free electrons in a metal if the density of free el...
A battery of emf $6\text{ V}$ and internal resistance $1\ \Omega$ is connected to a resistor. The current in the circuit is $0.5\text{ A}$. Calculate (i) the resistance of the resistor and (ii) the terminal voltage of the battery.
Assertion (A) : In a Wheatstone bridge circuit, if we interchange the position of the cell and the galvanometer, the balance condition $\frac{P}{Q} = \frac{R}{S}$ remains unchanged.
Reason (R) : $\frac{P}{Q} = \frac{R}{S} \Rightarrow \frac{Q}{S} = \frac{P}{R}$ so balance condition remains same.
(ii) The current in the 10 $\Omega$ resistor is : (A) 0$\cdot$3 A (B) 0$\cdot$6 A (C) 0$\cdot$2 A (D) 0
The current in the 10 $\Omega$ resistor is :
(A) 0.3 A
(B) 0.6 A
(C) 0.2 A
(D) 0
(ii) The current in the $10 \, \Omega$ resistor is : (A) $0.3 \, \text{A}$ (B) $0.6 \, \text{A}$ (C) $0.2 \, \text{A}$ (D) 0
Two wires of same length and same area of cross-section but made of different material of resistivities $\rho_1$ and $\rho_2$ are connected in series. The equivalent resistivity of the combination is :
(A) $\frac{1}{2}(\rho_1 + \rho_2)$
(B) $\rho_1 + \rho_2$
(C) $\sqrt{\rho_1\rho_2}$
(D) $2(\rho_1 +...
State Kirchhoff's rules. Using these rules, find the current flowing through branch FC in the given circuit.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.
(i) If resistor X were made of manganin and readings for V and I are taken without switching off the circuit, the grap...
Which of the following characteristics of electrons determines the current in the conductor ?
(A) Drift velocity only
(B) Thermal velocity only
(C) Both drift velocity and thermal velocity
(D) Neither drift nor thermal velocity
(a) The two Kirchhoff's rules are based on law of conservation of two physical quantities. Name the quantities.
(b) Find magnitude and direction of current in $1\ \Omega$ resistor in the given circuit.
The resistivity $\rho$ of a metal increases with rise in temperature because :
(A) only relaxation time '$\tau$' of electrons decreases with temperature.
(B) only number of electrons per unit volume '$n$' increases appreciably.
(C) '$\tau$' decreases with temperature but '$n$' does not change apprec...
A galvanometer of resistance $G$ is converted into a voltmeter of range $(0 - V)$ by connecting a resistor of $250\ \Omega$ with it. If resistor of $250\ \Omega$ is replaced by another resistor of $900\ \Omega$, its range becomes $(0 - 3\text{ V})$. The resistance $G$ of the galvanometer is :
(A) $1...
(a) 'Current is a scalar quantity, although we represent current with an arrow.' Explain.
(b) Derive the balance condition of a Wheatstone Bridge.
(a) (i) Derive the condition for which a Wheatstone Bridge is balanced.
(ii) Determine the current in $3\ \Omega$ branch of a Wheatstone Bridge in the circuit shown in the figure.
OR
(b) (i) Consider a cylindrical conductor of length $l$ and area of cross-section $A$. Current $I$ is maintained in ...
33. (a) (i) Derive the condition for which a Wheatstone Bridge is balanced.
(ii) Determine the current in $3\ \Omega$ branch of a Wheatstone Bridge in the circuit shown in the figure.
(b) (i) Consider a cylindrical conductor of length $l$ and area of cross-section $A$. Current $I$ is maintained in the conductor and electrons drift with velocity $v_d$ ($|\vec{v}_d| = \frac{e|\vec{E}|}{\text{m}}\tau$), (where symbols have their usual meanings). Show that the conductivity $\sigma$ o...
(a) (i) Derive the condition for which a Wheatstone Bridge is balanced.
(ii) Determine the current in $3\;\Omega$ branch of a Wheatstone Bridge in the circuit shown in the figure.
OR
(b) (i) Consider a cylindrical conductor of length $l$ and area of cross-section $A$. Current $I$ is maintained in the conductor and electrons drift with velocity $\vec{v_d}$ ($|\vec{v_d}...
A coil contains N turns of insulated copper wire of diameter d and resistivity $\rho$ wound on a cylinder of diameter D. What is the total resistance between the two ends of the coil of copper wire? (given: D>>d)
(A) $\frac{4\rho ND}{d^2}$
(B) $\frac{8\rho ND}{d^2}$
(C) $\frac{2\rho ND}{d^2}$
(D...
(I) The current $I_1$ in a wire is getting divided in two wires with currents $I_2$ and $I_3$ at a junction in a circuit. The currents in the three wires are related by $I_1 = I_2 + I_3$.
(A) State the fundamental law from which this relation is derived.
(B) Explain the validation of law of conserv...
(A) State the working principle of a moving coil galvanometer? What modification is required in the galvanometer to make its scale linear?
(B) If a galvanometer of resistance $49.5\,\Omega$ has range of $0.05\,\text{A}$. What will be the value of resistance needed to convert it in ammeter of range $...
A battery of emf $6\cdot0\text{ V}$ and internal resistance $0\cdot40\text{ }\Omega$ is connected to an external resistor of resistance $11\cdot6\text{ }\Omega$. The power dissipated in the external resistance is :
(A) $1\cdot45\text{ W}$
(B) $2\cdot9\text{ W}$
(C) $5\cdot8\text{ W}$
(D) $11\cdot6\t...
(ii) A conductor of length L is connected to a battery of emf E. This conductor is replaced by another conductor of the same material and the same cross-sectional area, but of length 2L. How will the drift speed change ?
OR
(b) (i) What is meant by internal resistance of a cell ? Name any two fact...
A current flows through a cylindrical conductor of radius $R$. The current density at a point in the conductor is $j = \alpha r$ (along its axis), here $\alpha$ is a constant and $r$ is distance from the axis of the conductor. The current flowing through the portion of the conductor from $r = 0$ to ...
(a) In the given figure, three identical bulbs $ ext{P}$, $ ext{Q}$ and $ ext{S}$ are connected to a battery.
(i) Compare the brightness of bulbs $ ext{P}$ and $ ext{Q}$ with that of bulb $ ext{S}$ when key $ ext{K}$ is closed.
(ii) Compare the brightness of the bulbs $ ext{S}$ and $ ext{Q}$ when th...
(ii) The above battery sends a current $I_1$ when $R = R_1$ and a current $I_2$ when $R = R_2$. Obtain the internal resistance of the battery in terms of $I_1$, $I_2$, $R_1$ and $R_2$.
The resistance of a wire at $25^{\circ}\text{C}$ is $10\cdot 0\ \Omega$. When heated to $125^{\circ}\text{C}$, its resistance becomes $10\cdot 5\ \Omega$. Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at $425^{\circ}\text{C}$.
Find the effective resistance of the network of resistors between points A and F as shown in the figure.
What is the difference between 'emf' and 'terminal voltage' of a cell?
Two cells of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ are connected in parallel. Derive an expression for the emf and internal resistance of the equivalent cell.
If $\text{R}_{\text{s}}$ and $\text{R}_{\text{p}}$ are the equivalent resistances of $\text{n}$ resistors, each of value $\text{R}$, in series and parallel combinations respectively, then the value of $(\text{R}_{\text{s}} - \text{R}_{\text{p}})$ is :
(A) $\left(\frac{\text{n}^2 - 1}{\text{n}^2}\rig...
A cell of emf $E$ and internal resistance $r$ is connected to an external variable resistance $R$. Plot a graph showing the variation of terminal voltage $V$ of the cell as a function of current $I$, supplied by the cell. Explain how the emf of the cell and its internal resistance can be found from ...
(a) Define the term 'drift velocity' of conduction electrons in a conductor.
(b) A conductor of length $l$ and area of cross-section A is connected across an ideal battery of emf V. Derive the formula for the current density in terms of relaxation time $\tau$.
(a) What is the difference between 'velocity' and 'drift velocity' of electrons in a current-carrying conductor.
(b) A copper wire of uniform cross-sectional area carries a current of $3.4 \text{ A}$. The drift velocity of conduction electrons is $0.2 \text{ mm/s}$. If the number density of electron...
State Kirchhoff's laws. Apply these laws to find the values of current flowing in the three branches of the given circuit.
A cell of emf $E$ and internal resistance $r$ is connected across a resistor of variable resistance $R$. Show graphically the variation of
(a) the terminal voltage across the cell,
(b) the current supplied by the cell,
with $R$ as it is increased from $0$ to the maximum value.
Three cells A, B and C of emfs $2\text{ V}$, $3\text{ V}$ and $5\text{ V}$ respectively are connected in parallel to each other. Their internal resistances are $5\text{ }\Omega$, $5\text{ }\Omega$ and $1\text{ }\Omega$ respectively. Calculate the currents flowing through the cells A, B and C.
The temperature coefficient of resistance of nichrome is $1.70 \times 10^{-4}\text{ }^\circ\text{C}^{-1}$. In order to increase resistance of a nichrome wire by $8.5%$, the temperature of the wire should be increased by :
(A) $250\text{ }^\circ\text{C}$
(B) $500\text{ }^\circ\text{C}$
(C) $850\text{...
Define the term 'drift velocity' of electrons in a current carrying conductor and derive, in its term, the expression for current flowing through the conductor.
Define 'emf' of a cell. Derive expression for the equivalent emf and the equivalent internal resistance of two cells connected in series.
Two cells are connected in parallel by connecting their positive terminals together and connecting their negative terminals together. Derive expression for the equivalent emf and the equivalent internal resistance of the combination.
Consider the circuit shown in the figure. The potential difference between points A and B is :
[Circuit diagram showing point A connected to two parallel branches. Top branch: $12\text{ V}$ battery and $1\text{ }\Omega$ resistor. Bottom branch: $6\text{ V}$ battery and $0.5\text{ }\Omega$ resistor. ...
Find the temperature at which the resistance of a wire made of silver will be twice its resistance at $20^\circ\text{C}$. Take $20^\circ\text{C}$ as the reference temperature and temperature coefficient of resistance of silver at $20^\circ\text{C} = 4\cdot 0 \times 10^{-3} \text{ K}^{-1}$.
Show that $\vec{E} = \rho \vec{j}$ leads to Ohm's law. Write a condition in which the Ohm's law is not valid for a material.
(a) Two batteries of emf's 3V & 6V and internal resistances 0.2 Ω & 0.4 Ω are connected in parallel. This combination is connected to a 4 Ω resistor. Find :
(i) the equivalent emf of the combination
(ii) the equivalent internal resistance of the combination
(iii) the current drawn from the combinati...
(b) (i) A conductor of length $l$ is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to $2l$ by gradually stretching it. If R and $R'$ are initial and final values of resistance and $v_d$ and $v_d'$ are initial and final values of drift v...
A student has three resistors, each of resistance R. To obtain a resistance of $\frac{2}{3} R$, she should connect (A) all the three resistors in series. (B) all the three resistors in parallel. (C) two resistors in series and then this combination in parallel with the third resistor. (D) two resist...
The threshold voltage of a silicon diode is $0.7 \text{ V}$. It is operated at this point by connecting the diode in series with a battery of $V$ volt and a resistor of $1000 \text{ } \Omega$. Find the value of $V$ when the current drawn is $15 \text{ mA}$.
(a) A cell of e.m.f. $E$ and internal resistance $r$ is connected with a variable external resistance $R$ and a voltmeter showing potential drop $V$ across $R$. Obtain the relationship between $V, E, R$ and $r$. (b) Draw the shape of the graph showing the variation of terminal voltage $V$ of the cel...
A battery of e.m.f. $12\text{ V}$ and internal resistance $0.5\text{ }\Omega$ is connected to a $9.5\text{ }\Omega$ resistor through a key. The ratio of potential difference between the two terminals of the battery, when the key is open to that when the key is closed, is
(A) $1.05$
(B) $1$
(C) $0.95...
The threshold voltage of a silicon diode is 0.7 V. It is operated at this point by connecting the diode in series with a battery of V volt and a resistor of 1000 $\Omega$. Find the value of V when the current drawn is 15 mA.
(a) Define resistivity of a conductor. Discuss its dependence on temperature of the conductor and draw a plot of resistivity of copper as a function of temperature.
(b) (i) "A low voltage battery from which high current is required must have low internal resistance." Justify.
(ii) "A high voltage ba...
Which pair of readings of ideal voltmeter and ideal ammeter in the given circuit is possible when a suitable power source of $3\text{ }\Omega$ internal resistance is connected between P and Q ?
(A) $12.0\text{ V}, 2.0\text{ A}$
(B) $2.0\text{ V}, 0.5\text{ A}$
(C) $6.0\text{ V}, 2.0\text{ A}$
(D) $1...
The threshold voltage of a silicon diode is $0.7\text{ V}$. It is operated at this point by connecting the diode in series with a battery of $\text{V}$ volt and a resistor of $1000\text{ }\Omega$. Find the value of $\text{V}$ when the current drawn is $15\text{ mA}$.
(a) Define Electrical conductivity. Obtain the expression of electrical conductivity of a conductor in terms of number density and relaxation time of free electrons. (b) Explain qualitative change in resistivity of a conductor with temperature using expression obtained in (a).
The resistance of a wire at $20 ext{ }^\circ ext{C}$ is $50 ext{ }\Omega$. When it is heated to $120 ext{ }^\circ ext{C}$, the resistance becomes $51 ext{ }\Omega$. The temperature coefficient of resistance of the material of the wire is
(A) $2 imes 10^{-4} ext{ }^\circ ext{C}^{-1}$
(B) $1 imes 10...
A $20.0\text{ cm}$ long wire is connected across an ideal battery of $4\text{ V}$. The drift velocity of conduction electrons in the wire is $0.8\text{ mm/s}$. Calculate the relaxation time of the electrons.
(a) Define the terms 'emf' and 'terminal voltage' of a cell. Can the terminal voltage of a cell ever exceed its emf? Explain.
OR
(b) Define the term current density. Write its SI unit. Derive the equivalent form of Ohm's law $\vec{j} = \sigma\vec{E}$.
(a) Define the term 'resistivity of a material'.
(b) Explain briefly how is the resistivity of (i) a metal and (ii) a semiconductor affected with the rise of temperature. Justify your answer.
A student is asked to connect four cells, each of emf E and internal resistance r, in series. But she/he connects one cell wrongly in series with the other cells. The equivalent emf and the equivalent internal resistance of the combination will be : (A) 4E and 2r (B) 4E and 3r (C) 3E and 4r (D) 2E a...
(a) Define current density. Is it a scalar or a vector ? An electric field $\vec{\text{E}}$ is maintained in a metallic conductor. If $\text{n}$ be the number of electrons (mass $\text{m}$, charge $-e$) per unit volume in the conductor and $\tau$ its relaxation time, show that the current density $\...
(I) a) Write two limitations of ohm's law. Plot their I-V characteristics. b) A heating element connected across a battery of $100\text{ V}$ having an internal resistance of $1\text{ }\Omega$ draws an initial current of $10\text{ A}$ at room temperature $20.0\text{ }^\circ\text{C}$ which settles aft...
(for V.I. Candidates) (II) a) Using Kirchhoff's laws obtain the equation of the balanced state in Wheatstone bridge.
A resistor and an ideal inductor are connected in series to a $100\sqrt{2}\text{ V}$, $50\text{ Hz}$ ac source. When a voltmeter is connected across the resistor or the inductor, it shows the same reading. The reading of the voltmeter is :
(A) $100\sqrt{2}\text{ V}$
(B) $100\text{ V}$
(C) $50\sqrt{2...
Define resistivity of a conductor. How does the resistivity of a conductor depend upon the following :
(a) Number density of free electrons in the conductor (n)
(b) Their relaxation time ($\tau$)
(a) "The electron drift speed is only a few mm/s for currents in the range of a few amperes for a given conductor." How then is current established almost the instant a circuit is closed ? Explain.
(b) 'V = IR is a statement of Ohm's Law' is not true. Explain.
Five identical cells, each of emf 2 V and internal resistance 0.1 $\Omega$ are connected in parallel. This combination in turn is connected to an external resistor of 9.98 $\Omega$. The current flowing through the resistor is :
(A) 0.05 A
(B) 0.1 A
(C) 0.15 A
(D) 0.2 A
Two conducting wires of same material have radii $r$ and $\frac{r}{2}$. The current flowing through them is $I$ and $2I$, respectively. Find the ratio of drift velocity of free electrons in the wires.
A galvanometer is converted into a voltmeter of range $(0 - V)$ volt using a resistor of $9900 \; \Omega$. If a resistor of $4900 \; \Omega$ is used, the range becomes half, i.e. $$0 - \frac{V}{2}$$ volt. Calculate : (a) resistance of the galvanometer (b) resistance required to convert it into a vol...
(a) A cell is connected across an external resistance $12 \Omega$ and supplies $0.25 \text{ A}$ current. When the external resistance is increased by $4 \Omega$, the current reduces to $0.2 \text{ A}$. Calculate (i) the emf, and (ii) the internal resistance, of the cell.
Two cells of emf $2 \text{ V}$ and $3 \text{ V}$, and internal resistance $1 \ \Omega$ and $2 \ \Omega$, respectively are connected in parallel. The effective emf and internal resistance of the combination cell are respectively :
(A) $3 \text{ V}, 1 \ \Omega$
(B) $5 \text{ V}, 3 \ \Omega$
(C) $\frac...
(a) A cell is connected across an external resistance $12 \,\Omega$ and supplies $0.25 \text{ A}$ current. When the external resistance is increased by $4 \,\Omega$, the current reduces to $0.2 \text{ A}$. Calculate (i) the emf, and (ii) the internal resistance, of the cell.
A battery of unknown emf E and internal resistance r is connected in a circuit as shown in the figure. When the key (K) is open, the voltmeter reads $10\cdot 0\text{ V}$ and ammeter reads $0\text{ A}$. In the closed circuit, the voltmeter reads $6\cdot 0\text{ V}$ and ammeter reads $2\cdot 0\text{ A...
Find the temperature at which the resistance of a conductor increases by 25% of its value at $27^{\circ}\text{C}$. The temperature coefficient of resistance of the conductor is $2.0 \times 10^{-4} ^{\circ}\text{C}^{-1}$.
A battery supplies $0.9 \text{ A}$ current through a $2 \text{ } \Omega$ resistor and $0.3 \text{ A}$ current through a $7 \text{ } \Omega$ resistor when connected one by one. The internal resistance of the battery is :
(A) $2 \text{ } \Omega$
(B) $1.2 \text{ } \Omega$
(C) $1 \text{ } \Omega$
(D) $0...
A galvanometer of resistance $50 \text{ } \Omega$ is converted into a voltmeter of range $(0 - 2\text{V})$ using a resistor of $1.0 \text{ k}\Omega$. If it is to be converted into a voltmeter of range $(0 - 10 \text{ V})$, the resistance required will be
(A) $4.8 \text{ k}\Omega$
(B) $5.0 \text{ k}\...
An ammeter and a voltmeter are connected in series to a battery. Their readings are noted as 'A' and 'V' respectively. If a resistor is connected in parallel with the voltmeter, then
(A) A will increase, V will decrease.
(B) A will decrease, V will increase.
(C) Both A and V will decrease.
(D) Both ...
(i) Define ‘temperature coefficient of resistance’ of a metal.
(ii) Show the variation of resistivity of copper with rise in temperature.
(iii) The resistance of a wire is $10 \ \Omega$ at $27 \ ^{\circ}\text{C}$. Find its resistance at $-73 \ ^{\circ}\text{C}$. The temperature coefficient of resist...
The emf and internal resistance of a cell are 3 V and $0.2 \ \Omega$ respectively. It is connected to an external resistor of $5.8 \ \Omega$. The potential difference across the cell will be : (A) 1.2 V (B) 2.0 V (C) 2.9 V (D) 3.2 V
Two identical cells, each of emf E and internal resistance r, are connected in series with a resistor of 8 $\Omega$. A current of 1.5 A flows in the circuit. When these cells are connected in parallel, they send 1.0 A current through the same resistor. Calculate the internal resistance, r and emf, E...
(a) Define the terms – 'temperature coefficient of resistance' and 'electrical conductivity' of a conductor. Why are constantan and manganin used for making standard resistances ? Explain.
OR (b) Define 'drift velocity'. Show that resistivity of the material of a conductor is inversely proportional to the relaxation time for the free electrons in the conductor.
A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0 °C and the temperature coefficient of resistance of nichr...
Name the factors on which electrical conductivity of a material depends. Obtain the relation between current density in a conductor and the conductivity of its material.
32. (a) (i) Derive the relation between the current and the drift velocity of free electrons in a conductor. Briefly explain the variation of resistance of a conductor with rise in temperature.
(ii) An ammeter, together with an unknown resistance in series is connected across two identical batteries...
OR
(b) (i) State Kirchhoff's rules. Use them to obtain the condition of balance for a Wheatstone Bridge.
(ii) Use Kirchhoff's rule to determine the currents flowing through the branches MN, TO and SP in the circuit shown in the figure.
Two cells, one of emf $2E$ and internal resistance $r$ and the other of emf $E$ and internal resistance $r/2$ are connected in parallel, by connecting their positive terminals together and their negative terminals together. The equivalent emf of the combination is :
(a) $3E$
(b) $\frac{4E}{3}$
(c) $...
Which of the following has a negative temperature coefficient of resistivity ?
(a) Silver
(b) Copper
(c) Nichrome
(d) Germanium
A cylindrical conductor of resistance $R$ is connected to a battery. The drift velocity of electrons in this conductor is $v_d$. The conductor is disconnected from the battery and gradually stretched so that its length increases by $25%$. It is again connected to the same battery. Find the new value...
The temperature ($T$) dependence of resistivity of materials A and material B is represented by fig (i) and fig (ii) respectively. Identify material A and material B.
(i) material A is copper and material B is germanium
(ii) material A is germanium and material B is copper
(iii) material A is nichro...
The figure shows a piece of pure semiconductor $S$ in series with a variable resistor $R$ and a source of constant voltage $V$. Should the value of $R$ be increased or decreased to keep the reading of the ammeter constant, when semiconductor $S$ is heated? Justify your answer
OR
The graph of poten...
(a) Explain the term drift velocity of electrons in a conductor. Hence obtain the expression for the current through a conductor in terms of drift velocity.
(b) Two cells of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ respectively are connected in parallel as shown in the figure. D...