(a) A series combination of L, C and R is connected to an a.c. source. Using a phasor diagram, derive an expression for the impedance of the circuit and phase difference between V and I.
(b) Under what conditions the
(i) impedance of the circuit is minimum ?
(ii) Wattless current flows in the circui...
CBSE CLASS 12 • PHYSICS • CHAPTER 07
Alternating Current
69 distinct questions across 90 board paper set appearances (2022–2026).
(a) (i) A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when : (I) an iron bar is inserted inside the coil, and (II) the frequency of the source is decreased ? Justify your answers. Assume that in eac...
(a) (i) Define the terms (I) resonant frequency, and (II) power factor of a series LCR circuit. For what value of the power factor will the power dissipated in the circuit be maximum ?
(ii) An inductor of $\frac{5}{\pi}\text{ H}$, a capacitor of $\frac{50}{\pi}\text{ }\mu\text{F}$ and a resistor of ...
(a) Using a phasor diagram, derive an expression for the impedance of a series LCR circuit connected to an ac source. What is meant by resonance in this circuit ? Obtain expression for the resonant frequency of this circuit.
An alternating current is given by $I = I_0 \cos $100\pi$ t$. The least time the current takes to decrease from its maximum value to zero will be :
(A) $\left(\frac{1}{200}\right)\text{ s}$
(B) $\left(\frac{1}{150}\right)\text{ s}$
(C) $\left(\frac{1}{100}\right)\text{ s}$
(D) $\left(\frac{1}{50}\ri...
Assertion (A) : In an ideal step-down transformer, the electrical energy is not lost.
Reason (R) : In a step-down transformer, voltage decreases but the current increases.
(a) (i) Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing variation of impedance of a series LCR circuit with the frequency of the applied a.c. source. (ii) With the help of a suitable diagram, explain the working of a step-up transformer. (iii...
(a) (i) Write the principle of working of an ac generator. Draw its labelled diagram and explain its working.
(ii) A resistor of $400\text{ }\Omega$, an inductor of $\left$\frac{5}{\pi}\right$\text{ H}$ and a capacitor of $\left$\frac{50}{\pi}\right$\text{ }\mu\text{F}$ are joined in series across a...
(ii) An ideal transformer is designed to convert $50\text{ V}$ into $250\text{ V}$. It draws $200\text{ W}$ power from an ac source whose instantaneous voltage is given by $v_i = 20\sin$100\pi$t\text{ V}$. Find :
(I) rms value of input current.
(II) expression for instantaneous output voltage.
(III)...
(a) A $20\text{ }\mu\text{F}$ capacitor is connected to a $220\text{ V}$, $\frac{125}{\pi}\text{ Hz}$ ac source.
(i) Find the capacitive reactance and the peak value of current in the circuit.
(ii) If the frequency of the ac source is doubled, by what factor will the capacitive reactance and the cur...
(a) (i) A series combination of $L$, $C$ and $R$ is connected to an ac source $V = V_m \sin \omega t$. Obtain :
(I) the impedance of the circuit using phasor diagram,
(II) the expression for the instantaneous current $I$, and
(III) the phase relationship of current to the applied voltage.
(ii) Defin...
Which of the following assumptions has been used to obtain the relation $\frac{\text{v}_\text{s}}{\text{v}_\text{p}} = \frac{\text{N}_\text{s}}{\text{N}_\text{p}}$ for a transformer ?
(A) The resistance of the primary coil is large.
(B) The same flux links both the primary and the secondary coils.
(...
The alternating current I in an inductor is observed to vary with time t as shown in the graph for a cycle. Which one of the following graphs is the correct representation of wave form of voltage V with time t?
(a) (i) You are given three circuit elements X, Y and Z. They are connected one by one across a given ac source. It is found that V and I are in phase for element X. V leads I by $\left$\frac{\pi}{4}\right$$ for element Y while I leads V by $\left$\frac{\pi}{4}\right$$ for element Z. Identify elemen...
(c) A conducting rod of length $50\text{ cm}$, with one end pivoted, is rotated with angular speed of $60\text{ rpm}$ in a uniform magnetic field of $4.0\text{ mT}$ directed perpendicular to the plane of rotation of rod. Find the emf induced in the rod.
OR
(a) Draw a labelled diagram of a step-up ...
A series LCR circuit with $R = 3\ \Omega$, $X_{\text{C}} = 4\ \Omega$, $X_{\text{L}} = 8\ \Omega$ is connected to a $220\text{ V}$, $50\text{ Hz}$ ac source. The power factor for the circuit is
(A) $0.30$
(B) $0.45$
(C) $0.50$
(D) $0.60$
$110$ kW electric power is supplied to the primary coil of an ideal transformer. If the output voltage is $22$ kV, the output current will be :
(A) $50$ A
(B) $25$ A
(C) $5$ A
(D) $0.5$ A
(a) An ideal inductor consumes no electric power in an ac circuit. Explain.
OR
(b) Two co-axial circular identical loops A and B, carrying equal currents in the same direction are placed at some distance. If loop B is brought closer to loop A with a constant speed, what will happen to the currents i...
Assertion (A) : In a series LCR circuit at resonance, the impedance is equal to ohmic resistance (R) in the circuit. Reason (R) : At resonance, the capacitive reactance is not equal to the inductive reactance.
(a) Prove that in an ac circuit containing only a pure inductor, the voltage is ahead of the current in phase by $\frac{\pi}{2}$ radian. Hence define inductive reactance. (b) The instaneous value of a voltage (in volt) is given by $\text{E} = 140 \sin 314 \text{t}$, where $\text{t}$ is in seconds. F...
A series combination of circuit elements X and Y is connected across an ac source. It is found that the voltage is ahead of current in phase by $\frac{\pi}{4}$ radian. When element Y is replaced by element Z, the current leads the voltage by $\frac{\pi}{4}$ radian.
(a) Identify the elements X, Y and...
(a) Differentiate between inductive reactance, capacitive reactance and impedance of an ac circuit.
(b) An ideal inductor and an ideal capacitor are connected in series across an ac voltage. Plot a graph showing variation of net reactance of the circuit with frequency of the applied ac voltage.
(a) Can a transformer step up or step down dc power supply ?
(b) Can a step up transformer work as a step down transformer ?
(c) Does a step up transformer contradict the principle of conservation of energy ? Justify your answer.
If the phasor diagram for a device connected to AC supply is as shown in the fig, then which of the following statements is true?
(A) When the frequency of the AC source is increased than the impedance of the device decreases.
(B) This device behaves as conducting wire when connected across DC sour...
The emf generated by an AC generator is given by $V=V_0\sin\omega t$, where $\omega$ is angular frequency of armature of generator. What will be the emf if the angular frequency is doubled<br><br>(A) $V=V_0\sin 2\omega t$<br>(B) $V=2V_0\sin\omega t$<br>(C) $V=2V_0\sin 2\omega t$<br>(D) $V=V_0\sin\om...
(A) An input potential $V_{\text{in}} = 200\sin 100\pi t\,\text{V}$ is provided to an ideal transformer having $1000$ turns in primary coil and $100$ turns in secondary coil as shown in figure. The load circuit has a resistance of $4\,\Omega$, a capacitive reactance of $2\,\Omega$ and an inductive r...
Which of the following statements about transformers is not correct ?
(A) For ideal transformers, the output power is equal to the input power.
(B) A transformer can work for both alternating and direct voltages.
(C) For a step-up transformer, the voltage across the secondary coil is higher but the ...
An ammeter connected in series in an ac circuit reads $10\text{ A}$. The maximum value of current at any instant in the circuit is :
(A) $10\sqrt{2}\text{ A}$
(B) $\frac{10}{\sqrt{2}}\text{ A}$
(C) $\frac{10}{\pi}\text{ A}$
(D) $\frac{10}{\sqrt{2}\,\pi}\text{ A}$
OR\n\n(b) (i) Differentiate between peak and rms values of alternating current. How are they related ?
(ii) A current element X is connected across an ac source of emf $V = V_0 \sin 2\pi \nu t$. It is found that the voltage leads the current in phase by $\frac{\pi}{2}$ radian. If element X was replaced by element Y, the voltage lags behind the current in phase by $\frac{\pi}{2}$ radian.
(I) Identify...
(b) (i) Differentiate between peak and rms values of alternating current. How are they related ?
(ii) A current element X is connected across an ac source of emf $V = V_0 \sin 2\pi \nu t$. It is found that the voltage leads the current in phase by $\frac{\pi}{2}$ radian. If element X was replaced by...
A transformer is a device used for converting :
(A) high ac voltage and large ac current to low ac voltage and small ac current
(B) high ac voltage and small ac current to low ac voltage and small ac current
(C) low ac voltage and large ac current to high ac voltage and small ac current
(D) low ac v...
(b) (i) Write the principle of working of a transformer. With the help of a labelled diagram, explain the working of a step-up transformer.
(ii) An ideal transformer is designed to convert $50\text{ V}$ into $250\text{ V}$. It draws $200\text{ W}$ power from an ac source whose instantaneous voltage ...
(a) (i) Write the principle of working of an ac generator. Draw its labelled diagram and explain its working.
(ii) A resistor of $400 \; \Omega$, an inductor of $\left$\frac{5}{\pi}\right$ \text{ H}$ and a capacitor of $\left$\frac{50}{\pi}\right$ \mu\text{F}$ are joined in series across an ac sourc...
Which of the following assumptions has been used to obtain the relation $\frac{v_s}{v_p} = \frac{N_s}{N_p}$ for a transformer ?
(A) The resistance of the primary coil is large.
(B) The same flux links both the primary and the secondary coils.
(C) The resistance of secondary coil is large.
(D) The tr...
(a) A $20\text{ }\mu\text{F}$ capacitor is connected to a $220\text{ V}$, $\frac{125}{\pi}\text{ Hz}$ ac source.\n(i) Find the capacitive reactance and the peak value of current in the circuit.\n(ii) If the frequency of the ac source is doubled, by what factor will the capacitive reactance and the c...
(a) (i) A series combination of $L$, $C$ and $R$ is connected to an ac source $V = V_{\text{m}} \sin \omega t$. Obtain :
(I) the impedance of the circuit using phasor diagram,
(II) the expression for the instantaneous current $I$, and
(III) the phase relationship of current to the applied voltage.
(...
The ratio of the number of turns of the primary to the secondary coils in an ideal transformer is 20 : 1. If 240 V ac is applied from a source to the primary coil of transformer and a 6.0 $\Omega$ resistor is connected across the output terminals, then current drawn by the transformer from the sourc...
An ac source of voltage $v = v_m \sin \omega t$ is connected to a series combination of LCR circuit. Draw the phasor diagram. Using it obtain an expression for the impedance of the circuit and the phase difference between applied voltage and the current.
A transformer is connected to a 200 V ac source. The transformer supplies 3000 V to a device. If the number of turns in the primary coil is 450, then the number of turns in its secondary coil is - (A) 30 (B) 450 (C) 4500 (D) 6750
The alternating current I in an inductor is observed to vary with time $t$ as shown in the graph for a cycle.
[Graph of I versus t showing a triangular waveform peaking at $T/2$ and ending at $T$]
Which one of the following graphs is the correct representation of wave form of voltage $V$ with time...
Differentiate between the peak value and root mean square value of an alternating current. Derive the expression for the root mean square value of alternating current, in terms of its peak value.
A soft iron rod X is allowed to fall on the two poles of a U shaped permanent magnet as shown in figure. A coil is wrapped over one arm of the U shaped magnet.
During fall of the rod, the current in the coil will be
(A) clockwise current
(B) anticlockwise current
(C) alternating current
(D) zero
The number of turns between different pairs of output terminals are shown for a step-up transformer.
Input voltage of $20\text{ V}$ is applied between A and B. Between which two terminals will the output be $120\text{ V}$ ?
(A) P and Q
(B) Q and S
(C) P and R
(D) P and S
(a) ac voltage of frequency $\omega$ is applied across a series LCR circuit. Draw the phasor diagram and obtain the impedance of the circuit. (b) Discuss 'resonance' in a series LCR circuit and write the expression for resonant frequency.
A step up transformer —
(A) decreases the current to transmit power over short distances with minimum loss.
(B) increases the current to transmit power over short distances with minimum loss.
(C) increases the voltage to transmit power over short distances with minimum loss.
(D) increases the voltag...
Assertion (A) : At resonance the impedance of a series LCR circuit is $Z = R$.
Reason (R) : $Z = \sqrt{R^2 + (X_C - X_L)^2}$ and at resonance the inductive reactance ($X_L$) is equal to the capacitive reactance ($X_C$).
(a) Explain how the reactance of a capacitor and that of an inductor change with the frequency of ac source.
(b) An ideal inductor of self-inductance $0.5\text{ H}$ is connected to an ac source of peak voltage $314\text{ V}$ and frequency $50\text{ Hz}$. Calculate the peak value of current in the ci...
An alternating voltage of frequency of 50 Hz is applied to a half-wave rectifier. Then the ripple frequency of the output will be :
(A) 100 Hz
(B) 50 Hz
(C) 25 Hz
(D) 150 Hz
(iii) An electric lamp is designed to operate at 110 V dc and 11 A current. If the lamp is operated on 220 V, 50 Hz ac source with a coil in series, then find the inductance of the coil.
(b) (i) Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three causes for energy losses in a real transformer. (ii) A step-up transformer converts a low voltage into high voltage. Does it violate the principle of conservation of energy? Explain. (iii) ...
The primary and secondary coils of a transformer have 500 turns and 5000 turns respectively. The primary coil is connected to an ac source of 220 V - 50 Hz. The output across the secondary coil is : (A) 220 V - 50 Hz (B) 1100 V - 50 Hz (C) 2200 V - 5 Hz (D) 2200 V - 50 Hz
(a) Draw the graphs showing the variation of the following with the frequency of ac source in a circuit :
(i) Resistance
(ii) Capacitive reactance
(iii) Inductive reactance
(b) Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the applied voltage of t...
(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.
(iii) An electric lamp is designed to operate at $110\text{ V}$ ...
(I) Explain briefly, with the help of a labelled diagram, the basic principle of the working of an a.c. generator. In an a.c. generator, coil of $N$ turns and area $A$ is rotated at an angular velocity $\omega$ in a uniform magnetic field $B$. Derive an expression for the instantaneous value of the ...
In an ac circuit, the instantaneous values of current (in A) and voltage (in V) are $\text{I} = 5 \sin \omega\text{t}$ and $\text{E} = 200 \cos$\omega\text{t} + \frac{\pi}{3}$$ respectively. The phase difference between voltage and current at any instant is :
(A) $\frac{5\pi}{6}$
(B) $\frac{5\pi}{4}...
An ac voltage $v_i = 140 \sin$100 \pi t$ \text{ V}$ is applied to the primary coil having 200 turns, of an ideal transformer and it supplies a power of 5 kW. If the secondary coil has 1000 turns, find:
(a) the output voltage,
(b) the instantaneous voltage across the secondary coil, and
(c) the curre...
A bulb is rated $(100 \; \text{W}, 110 \; \text{V})$. It is operated by current of $1.0 \; \text{A}$ supplied by a step down transformer. If the input voltage and efficiency of the transformer are $220 \; \text{V}$ and $0.9$ respectively, the input current drawn from the mains is :
(A) $\frac{1}{2} ...
If the frequency of the half-wave rectifier is 50 Hz, the frequency of full-wave rectifier is :
(A) 25 Hz (B) 50 Hz
(C) 100 Hz (D) 200 Hz
A sinusoidal voltage is applied to an electric circuit containing a circuit element 'X' in which the current leads the voltage by $\frac{\pi}{2}$. (a) Identify the circuit element 'X' in the circuit. (b) Write the formula for its reactance. (c) Show graphically the variation of this reactance with f...
Distinguish between reactance and impedance of an ac circuit. Show that an ideal inductor in an ac circuit does not dissipate any power.
Figure shows the variation of inductive reactance $X_L$ of two ideal inductors of inductance $L_1$ and $L_2$, with angular frequency $\omega$. The value of $\frac{L_1}{L_2}$ is
(A) $\sqrt{3}$
(B) $\frac{1}{\sqrt{3}}$
(C) $3$
(D) $\frac{1}{3}$
(i) You are given three circuit elements X, Y and Z. They are connected one by one across a given ac source. It is found that V and I are in phase for element X. V leads I by $\left$\frac{\pi}{4}\right$$ for element Y while I leads V by $\left$\frac{\pi}{4}\right$$ for element Z. Identify elements X...
(i) Describe the construction and working of a transformer and hence obtain the relation for $\left(\frac{V_s}{V_p}\right)$ in terms of number of turns of primary and secondary. (ii) Discuss four main causes of energy loss in a real transformer.
OR (b) (i) Describe the construction and working of a transformer and hence obtain the relation for $\left(\frac{v_s}{v_p}\right)$ in terms of number of turns of primary and secondary. (ii) Discuss four main causes of energy loss in a real transformer.
OR (b) (i) Describe the construction and working of a transformer and hence obtain the relation for $\frac{v_s}{v_p}$ in terms of number of turns of primary and secondary. (ii) Discuss four main causes of energy loss in a real transformer.
Assertion (A) : The capacitive reactance increases with the increase of the frequency ($\omega$) of applied ac voltage.
Reason (R) : The value of capacitive reactance ($X_C$) is $\omega C$.
a. Draw graphs showing the variations of inductive reactance and capacitive reactance with frequency of applied ac source. b. Draw the phasor diagram for a series LRC circuit connected to an AC source. c. When an alternating voltage of $220\text{V}$ is applied across a device X, a current of $0.25\t...
(a) (i) Differentiate between the resistance and reactance of a series LCR circuit.
(ii) Explain how a capacitor blocks a direct current and an inductor opposes an alternating current.
OR
(b) Show mathematically that in an ac circuit containing a pure inductor, the current lags behind the voltage in...