Alternating Current — CBSE Class 12 board PYQs

An a.c. voltage is applied across an ideal inductor. The current in it

Laminated iron sheets are used to minimize ______ currents in the core of a transformer.

Define the 'quality factor' of resonance in a series LCR circuit. What is its S.I. unit?

Define capacitive reactance. Write its S.I. unit.

Why is the use of a.c. voltage preferred over d.c. voltage? Give two reasons.

Define the term 'wattless current'.

The instantaneous current and voltage of an a.c. circuit are given by $i=10\sin 300t$ A and $v=200\sin 300t$ V. What is the power dissipation in the circuit?

The instantaneous current and voltage of an a.c. circuit are given by $i=10\sin 314t$ A and $v=50\sin \left(314t+\frac{\pi }{2}\right)$ V. What is the power dissipation in the circuit?

What do you mean by the impedance of an LCR circuit?

In a series LCR circuit, the voltages across an inductor, a capacitor and a resistor are 30 V, 30 V and 60 V respectively. What is the phase difference between the applied voltage and the current in the circuit?

What do you mean by power factor? On what factors does it depend?

The power factor of an a.c. circuit is 0.5. What will be the phase difference between voltage and current in this circuit?

A bulb and a capacitor are connected in series to an a.c. source of variable frequency. How will the brightness of the bulb change on increasing the frequency of the a.c. source? Give reason.

In a series LCR circuit, the voltages across an inductor, a capacitor and a resistor are 20 V, 20 V and 40 V respectively. What is the phase difference between the applied voltage and the current in the circuit?

What is the power dissipated in an a.c. circuit in which the voltage and current are given by $V=230\sin \left(\omega t+\frac{\pi }{2}\right)$ and $I=10\sin \omega t$?

Peak value of emf of an a.c. source is $E_0$. What is its r.m.s. value?

A series RC circuit with $R=200\Omega$ and $C=\left(\frac{50}{\pi }\right)\mu \text{F}$ is connected across an a.c. source of peak voltage ${\epsilon }_0=100$ V and frequency $\nu =50$ Hz. Calculate
(a) the impedance of the circuit ($Z$),
(b) the phase angle ($\varphi$), and
(c) the …

A resistance R and a capacitor C are connected in series to a source $V=V_0\sin \omega t$. Find: (a) the peak value of the voltage across (i) the resistance and (ii) the capacitor; (b) the phase difference between the applied voltage and the current — which of them is ahead?

For the series LCR circuit shown, with $L=100\text{mH}$, $C=2\mu \text{F}$ and $R=400\Omega$ driven by $V=V_0\sin (1000t+\varphi )$:
(i) find the phase difference between the current and the voltage, and state which one leads in phase.
(ii) Without making any other change, find t …

(i) When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero.
(ii) A bulb is connected in series with a variable capacitor and an AC source as shown. What happens to the brightness of the bulb when the …

An inductor $L$ of inductive reactance $X_L$ is connected in series with a bulb B and an AC source. How would the brightness of the bulb change when
(i) the number of turns in the inductor is reduced,
(ii) an iron rod is inserted in the inductor, and
(iii) a capacitor of reacta …

(a) For a given a.c., $i=i_m\sin \omega t$, show that the average power dissipated in a resistor R over a complete cycle is $\frac{1}{2}{i}_m^{2}R$.
(b) A light bulb is rated at 125 W for a 250 V a.c. supply. Calculate the resistance of the bulb.

The figure shows a series LCR circuit with $L=10.0\text{H}$, $C=40\mu \text{F}$ and $R=60\Omega$ connected to a variable-frequency 240 V source. Calculate:
(i) the angular frequency of the source that drives the circuit at resonance,
(ii) the current at the resonating freque …

An alternating voltage of frequency $f$ is applied across a series LCR circuit. Let $f_r$ be the resonance frequency of the circuit. Will the current in the circuit lag, lead, or remain in phase with the applied voltage when
(i) $f>f_r$, and
(ii) $f<f_r$? Explain your a …

(i) State the law that gives the polarity of the induced e.m.f.
(ii) A $15.0\mu \text{F}$ capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance and the rms current.

Prove that an ideal inductor does not dissipate power in an a.c. circuit.

Distinguish between the terms 'average value' and 'rms value' of an alternating current. The instantaneous current from an a.c. source is $I=5\sin (314t)$ ampere. What are the average and rms values of the current?

Distinguish between the terms 'effective value' and 'peak value' of an alternating current. An alternating current from a source is represented by $I=10\sin (314t)$. Write the corresponding values of
(i) its effective value,
(ii) the frequency of the source.

Explain, with the help of a labelled diagram, the underlying principle and working of a step-up transformer. Why can such a device not be used to step up a d.c. voltage?

Draw a labelled diagram of an a.c. generator. Explain briefly its principle and working.

Given are two electric circuits A and B. In circuit A an inductor of reactance $X_L=3R$ is in series with a resistance $R$. In circuit B an inductor of reactance $X_L=3R$, a resistance $R$ and a capacitor of reactance $X_C=R$ are all in series. Calculate the ratio of the power fa …

An alternating voltage of frequency $f$ is applied across a series LCR circuit. Let $f_r$ be the resonance frequency for the circuit. Will the current in the circuit lag, lead or remain in phase with the applied voltage when
(i) $f>f_r$,
(ii) $f<f_r$? Explain your answer in each …

When an inductor L and a resistor R in series are connected across a 12 V, 50 Hz supply, a current of 0.5 A flows in the circuit. The current differs in phase from the applied voltage by $\frac{\pi }{3}$ radian. Calculate the value of R.

(i) Draw the graphs showing the variation of inductive reactance and capacitive reactance with the frequency of the applied a.c. source.
(ii) Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the applied voltage of the a.c. source? …

State the condition under which the phenomenon of resonance occurs in a series LCR circuit. Plot a graph showing the variation of current with the frequency of the a.c. source in a series LCR circuit.

Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing the variation of impedance of a series LCR circuit with the frequency of the applied a.c. source.

Explain, with the help of a diagram, the principle and working of an a.c. generator. Write the expression for the e.m.f. generated in the coil in terms of its speed of rotation.

A town situated $20\mathrm{km}$ away from a power plant generating power at $440\mathrm{V}$ requires $600\mathrm{kW}$ of electric power at $200\mathrm{V}$. The resistance of the two-wire line carrying power is $0.4\Omega$ per km. The town gets power from the line throug …

When an inductor $L$ and a resistor $R$ in series are connected across a $12\mathrm{V}$, $50\mathrm{Hz}$ supply, a current of $0.5\mathrm{A}$ flows in the circuit. The current differs in phase from the applied voltage by $\pi /3$ radian. Calculate the value of $R$.

(i) Draw the graphs showing the variation of inductive reactance and capacitive reactance with the frequency of the applied AC source.
(ii) Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the applied voltage of the AC source? Just …

(a)(i) You are given three circuit elements X, Y and Z. They are connected one by one across a given a.c. source. It is found that V and I are in phase for element X, V leads I by $\frac{\pi }{2}$ for element Y, while I leads V by $\frac{\pi }{2}$ for element Z. Identify the elemen …

(b)(i) Describe the construction and working of a transformer and hence obtain the relation for $\frac{V_s}{V_p}$ in terms of the number of turns of the primary and secondary. (ii) Discuss four main causes of energy loss in a real transformer.

(a) With the help of a labelled diagram, explain the working of a step-up transformer. Give reasons to explain the following: (i) the core of the transformer is laminated, (ii) thick copper wire is used in the windings. (b) A conducting rod PQ of length 20 cm and resistance …

(a) In a series LCR circuit connected across an a.c. source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with the frequency of the a.c. source.
(b) What is the phase difference between the voltages across the inductor and th …

(a) Draw the diagram of a device which is used to decrease a high a.c. voltage into a low a.c. voltage and state its working principle. Write four sources of energy loss in this device. (b) A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away fr …

Electrical energy is transmitted over long distances from a power generating station to a city in the form of alternating current (a.c.) raised to a high voltage; at the receiving end the voltage is reduced to operate the devices, and as a result the power loss is reduced.
(a) Na …

State the principle of an a.c. generator and explain its working with the help of a labelled diagram. Obtain the expression for the emf induced in a coil having N turns, each of cross-sectional area A, rotating with a constant angular speed $\omega$ in a magnetic field $\vec{B}$ …

A device X is connected across an a.c. source of voltage $V=V_0\sin \omega t$. The current through X is $I=I_0\sin \left(\omega t+\frac{\pi }{2}\right)$. (a) Identify the device X and write the expression for its reactance. (b) Draw graphs showing the variation of voltage and curr …

In the circuit shown, a resistor $R=10\Omega$ and an inductor $L=200\text{mH}$ are connected in series with a capacitor $C$ and an a.c. source of rms voltage 50 V and angular frequency $100{\text{s}}^{-1}$. Calculate
(a) the capacitance of the capacitor if the power factor of …

(a) Prove that the current flowing through an ideal inductor connected across an a.c. source lags the voltage in phase by $\frac{\pi }{2}$.
(b) An inductor of self-inductance 100 mH and a bulb are connected in series with an a.c. source of rms voltage 10 V, 50 Hz. It is found tha …

(a) Draw a labelled diagram of an a.c. generator and derive the expression for the instantaneous value of the emf induced in the coil.
(b) A circular coil of cross-sectional area $200{\text{cm}}^2$ and 20 turns is rotated about its vertical diameter with an angular speed of …

(a) Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of the number of turns and currents in the two coils.
(b) A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings hav …

(a) An AC source of voltage $V=V_0\sin \omega t$ is connected to a series combination of $L$, $C$ and $R$. Use a phasor diagram to obtain expressions for the impedance of the circuit and the phase angle between the voltage and the current. Find the condition for the current to …

(a) Write the function of a transformer. State its principle of working with the help of a diagram, and mention the various energy losses in this device. (b) The primary coil of an ideal step-up transformer has $100$ turns and the transformation ratio is also $100$. The input vol …

In a series LCR circuit connected to an AC source of voltage $v=v_m\sin \omega t$, use a phasor diagram to derive an expression for the current in the circuit. Hence obtain the expression for the power dissipated in the circuit, and show that the power dissipated at resonance …

At a substation a box is marked "Danger — H.T. 2200 V".
(i) Which device is used to bring a high AC voltage down to a low AC voltage, and what is the principle of its working?
(ii) Is it possible to use this device to bring a high DC voltage down to a low voltage? Explain.

A voltage $V=V_0\sin \omega t$ is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle. Under what condition is
(i) no power dissipated even though a current flows through the circuit,
(ii) maximum power dissipated in the circuit?

State the working of an a.c. generator with the help of a labelled diagram. The coil of an a.c. generator having N turns, each of area A, is rotated with a constant angular velocity $\omega$. Deduce the expression for the alternating e.m.f. generated in the coil. What is the sour …

Describe briefly, with the help of a labelled diagram, the basic elements of an a.c. generator. State its underlying principle. Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous val …

A series LCR circuit is connected to a source having voltage $v=v_m\sin \omega t$. Derive the expression for the instantaneous current $I$ and its phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define 'power factor' and state the conditions …

(a) Derive an expression for the average power consumed in a series LCR circuit connected to an a.c. source in which the phase difference between the voltage and the current is $\varphi$.
(b) Define the quality factor of an a.c. circuit. Why should the quality factor have a high val …

(a) Derive the relationship between the peak value and the rms value of current in an a.c. circuit.
(b) Describe briefly, with the help of a labelled diagram, the working of a step-up transformer. A step-up transformer converts a low voltage into a high voltage. Does it not viola …

The given circuit diagram shows a series LCR circuit with $L=5.0\text{H}$, $C=80\mu \text{F}$ and $R=40\Omega$ connected to a variable-frequency 230 V source. (a) Determine the source frequency which drives the circuit in resonance. (b) Obtain the impedance of the circuit an …

The primary coil of an ideal step-up transformer has 100 turns and the transformation ratio is also 100. The input voltage and power are 220 V and 1100 W respectively. Calculate:
(i) the number of turns in the secondary,
(ii) the current in the primary,
(iii) the voltage across t …