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Alternating Current Set-4 MCQ Online Practice Test | Class 12 | Quiz Tweek

Alternating Current Set-4

Practice Important MCQs for Alternating Current — Physics, Class 12.

Alternating Current (AC) is central to understanding real power transfer, impedance, power factor correction, and resonance in LCR circuits. Board as well as competitive exams repeatedly test concepts like phase difference, rms values, resonance conditions (series and parallel), and how non-sinusoidal signals affect power using harmonic orthogonality.

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Q1. A series $RC$ circuit has $R=50\ \Omega$ and $C=100\ \mu\text{F}$ connected to an AC source of $V_{\text{rms}}=230\ \text{V}$ at $f=50\ \text{Hz}$ . Using $X_C=\dfrac{1}{\omega C}$ , $Z=\sqrt{R^2+X_C^2}$ and $I_{\text{rms}}=\dfrac{V_{\text{rms}}}{Z}$ , the RMS current in the circuit is:

(A)

$3.02\ \text{A}$

(B)

$3.88\ \text{A}$

(C)

$4.60\ \text{A}$

(D)

$2.31\ \text{A}$

Q2. A series $RL$ circuit with $R=40\ \Omega$ and $L=200\ \text{mH}$ is connected to a sinusoidal source of $V_{\text{rms}}=220\ \text{V}$ at $f=50\ \text{Hz}$ . Using $X_L=\omega L$ , $Z=\sqrt{R^2+X_L^2}$ and $\cos\phi=\dfrac{R}{Z}$ , the average power absorbed by the circuit and the phase angle between source voltage and current (positive = current lags) are closest to:

(A)

$P=220\ \text{W},\ \phi=45^\circ\ \text{(lagging)}$

(B)

$P=698\ \text{W},\ \phi=32^\circ\ \text{(lagging)}$

(C)

$P=262\ \text{W},\ \phi=48^\circ\ \text{(lagging)}$

(D)

$P\approx 349\ \text{W},\ \phi\approx 57.5^\circ\ \text{(lagging)}$

Q3. A single‑phase load draws $P=10\ \text{kW}$ at $V_{\text{rms}}=230\ \text{V}$ with power factor $\cos\phi_1=0.60$ (lagging). A capacitor is connected in parallel to improve the overall power factor to $\cos\phi_2=0.95$ at $f=50\ \text{Hz}$ . The required capacitance $C$ (approx.) is:

(A)

$605\ \mu\text{F}$

(B)

$303\ \mu\text{F}$

(C)

$150\ \mu\text{F}$

(D)

$1.21\ \text{mF}$

Q4. Consider a series $RLC$ circuit driven at its resonance frequency $\omega_0=\dfrac{1}{\sqrt{LC}}$ with a very small $R$ (high $Q$ ). Statement I: "Magnitudes of voltages across $L$ and $C$ can individually be much larger than the applied voltage at resonance." Statement II: "This occurs because at resonance $X_L=X_C$ so a large current (limited mainly by $R$ ) flows; the large reactive drops $V_L=I X_L$ and $V_C=I X_C$ are $180^\circ$ out of phase and largely cancel, leaving a relatively small supply voltage." Which of the following is correct?

(A)

I is true and II is false

(B)

I is false and II is true

(C)

Both I and II are true and II correctly explains I

(D)

Both I and II are true but II does not correctly explain I

Q5. A non‑sinusoidal voltage is applied across a resistor $R=10\ \Omega$ :

v(t)=170\sin(100\pi t)+85\sin(300\pi t)\ \text{(V)}.

Calculate the average power dissipated in the resistor (use orthogonality of different harmonics).

(A)

$1445.0\ \text{W}$

(B)

$1806.25\ \text{W}$

(C)

$361.25\ \text{W}$

(D)

$2890.0\ \text{W}$

Q6. A series RL circuit is connected to an AC source $v(t)=220\sqrt{2}\sin(100\pi t)$ . The resistor is $R=44\ \Omega$ and the inductor $L=0.22\ \mathrm{H}$ . The average (real) power dissipated in the circuit is:

(A)

$220\ \mathrm{W}$

(B)

$440\ \mathrm{W}$

(C)

$317.4\ \mathrm{W}$

(D)

$158.7\ \mathrm{W}$

Q7. In a series LCR circuit $R=40\ \Omega$ , $L=0.20\ \text{H}$ and $C=50\ \mu\text{F}$ . For what frequency $f$ (in Hz) does the circuit current lead the applied voltage by $30^\circ$ ?

(A)

$42.0\ \text{Hz}$

(B)

$60.4\ \text{Hz}$

(C)

$30.2\ \text{Hz}$

(D)

$75.0\ \text{Hz}$

Q8. A single‑phase load draws $P=12\ \text{kW}$ at a lagging power factor of $0.70$ from a $230\ \text{V}$ , $50\ \text{Hz}$ supply. A capacitor is connected in parallel to improve the overall power factor to $0.95$ (lagging). The capacitance required (approx.) is:

(A)

$200\ \mu\text{F}$

(B)

$800\ \mu\text{F}$

(C)

$50\ \mu\text{F}$

(D)

$500\ \mu\text{F}$

Q9. For a series LCR circuit with inductance $L$ and resistance $R$ , the capacitance is halved ( $C\to C/2$ ) and the resistance is doubled ( $R\to 2R$ ) while $L$ is unchanged. Which statement correctly describes the changes in (i) resonant angular frequency $\omega_0$ , (ii) quality factor $Q$ , and (iii) resonance current amplitude $I_{\mathrm{res}}$ (for a fixed source voltage amplitude)?

(A)

$\omega_0$ unchanged; ; $Q\to Q/2$ ; ; $I_{\mathrm{res}}$ unchanged

(B)

$\omega_0\to \sqrt{2}\,\omega_0$ ; ; $Q\to Q/\sqrt{2}$ ; ; $I_{\mathrm{res}}\to I_{\mathrm{res}}/2$

(C)

$\omega_0\to \sqrt{2}\,\omega_0$ ; ; $Q\to \sqrt{2}\,Q$ ; ; $I_{\mathrm{res}}\to I_{\mathrm{res}}/\sqrt{2}$

(D)

$\omega_0\to \omega_0/2$ ; ; $Q\to Q/2$ ; ; $I_{\mathrm{res}}\to I_{\mathrm{res}}/2$

Q10. A coil of inductance $L=0.50\ \text{H}$ and series resistance $r=1.0\ \Omega$ is connected in parallel with a capacitor such that the parallel network is driven at resonance $f=50\ \text{Hz}$ by a supply of $V_{\mathrm{rms}}=100\ \text{V}$ . At resonance, the magnitude of current through the inductor $I_L$ and the magnitude of the source current $I_s$ (approximately) are:

(A)

$I_L\approx 0.637\ \text{A},\; I_s\approx 4.05\ \text{mA}$

(B)

$I_L\approx 4.05\ \text{mA},\; I_s\approx 0.637\ \text{A}$

(C)

$I_L\approx 0.637\ \text{A},\; I_s\approx 63.7\ \text{mA}$

(D)

$I_L\approx 63.7\ \text{mA},\; I_s\approx 4.05\ \text{mA}$

Q11. A resistor $R=100\ \Omega$ is connected across an AC supply whose instantaneous voltage is $v(t)=220\sqrt{2}\sin(100\pi t)\ \text{V}$ . How much heat energy is dissipated in the resistor in $10$ minutes after connection?

(A)

$2.904\times10^{3}\ \text{J}$

(B)

$2.904\times10^{5}\ \text{J}$

(C)

$2.904\times10^{4}\ \text{J}$

(D)

$2.904\times10^{6}\ \text{J}$

Q12. A series $R$ – $L$ circuit has $R=30\ \Omega$ and is connected to an AC source of frequency $f=50\ \text{Hz}$ . The measured power factor of the circuit is $0.8$ . Calculate the inductance $L$ .

(A)

$1.43\times10^{-3}\ \text{H}$

(B)

$0.225\ \text{H}$

(C)

$7.16\times10^{-1}\ \text{H}$

(D)

$\dfrac{22.5}{100\pi}\ \mathrm{H}\approx 7.16\times10^{-2}\ \text{H}$

Q13. A resistor $R=40\ \Omega$ is connected in series with a capacitor $C=50\ \mu\text{F}$ across an AC source of $V_{\text{rms}}=100\ \text{V}$ at frequency $f=50\ \text{Hz}$ . The average power absorbed by the circuit is:

(A)

$7.084\times10^{1}\ \text{W}$

(B)

$1.331\times10^{2}\ \text{W}$

(C)

$2.667\times10^{1}\ \text{W}$

(D)

$2.50\times10^{2}\ \text{W}$

Q14. In a series RLC circuit with $R=10\ \Omega$ and $L=0.5\ \text{H}$ connected to an AC source of frequency $f=50\ \text{Hz}$ , the circuit is adjusted so that the current leads the applied voltage by $30^\circ$ . The required capacitance $C$ is:

(A)

$1.95\times10^{-6}\ \text{F}$

(B)

$26.6\ \mu\text{F}$

(C)

$1.955\times10^{-5}\ \text{F}\approx 19.6\ \mu\text{F}$

(D)

$9.75\ \mu\text{F}$

Q15. A non‑sinusoidal voltage $v(t)=100\sin(\omega t)+50\sin(3\omega t)\ \text{V}$ is applied across a resistor $R=25\ \Omega$ . The average power dissipated in the resistor is:

(A)

$125\ \text{W}$

(B)

$250\ \text{W}$

(C)

$375\ \text{W}$

(D)

$200\ \text{W}$

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