Power in AC Circuits — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Power in AC Circuits MCQs with step-by-step solutions (21 questions). Part of AC Circuits. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Power in AC Circuits · easy · theory
The average power consumed in an AC circuit is given by:
A. $V_{rms}I_{rms}\cos\phi$ ✓ Correct
B. $V_{rms}I_{rms}\sin\phi$
C. $V_0I_0\cos\phi$
D. $V_{rms}I_{rms}$
Solution: The factor $\cos\phi$ is the power factor; only the in-phase component of the current does net work.
Q2 — Power in AC Circuits · easy · theory
The power factor of an AC circuit is given by:
A. $\dfrac{R}{Z}$ ✓ Correct
B. $\dfrac{X_L}{Z}$
C. $\dfrac{R}{X_C}$
D. $\dfrac{Z}{R}$
Solution: It is the cosine of the phase angle, and equals unity for a purely resistive circuit.
Q3 — Power in AC Circuits · medium · theory
The current in a pure inductor or a pure capacitor is called a wattless current because:
A. The resistance is infinite
B. The current itself is zero
C. The average power consumed over a cycle is zero ✓ Correct
D. The voltage across it is zero
Solution: With $\phi = 90^\circ$, $\cos\phi = 0$; energy drawn in one quarter cycle is returned in the next.
Q4 — Power in AC Circuits · easy · theory
In a purely resistive AC circuit, the average power consumed is:
A. $V_{rms}I_{rms}$ ✓ Correct
B. $\dfrac{V_{rms}I_{rms}}{2}$
C. $V_0I_0$
D. Zero
Solution: The phase angle is zero, so the power factor is unity.
Q5 — Power in AC Circuits · medium · theory
At resonance, the power consumed by a series LCR circuit is:
A. Zero
B. Maximum, since the power factor is unity ✓ Correct
C. Independent of the resistance
D. Minimum
Solution: Both the current and the power factor are at their maximum values, so the power is greatest.
Q6 — Power in AC Circuits · medium · theory
The apparent power in an AC circuit is defined as:
A. $V_{rms}I_{rms}$, measured in volt-ampere ✓ Correct
B. $V_{rms}I_{rms}\cos\phi$, measured in watt
C. $I_{rms}^2R$
D. $V_{rms}I_{rms}\sin\phi$
Solution: Only the fraction $\cos\phi$ of the apparent power is actually consumed; the rest oscillates to and fro.
Q7 — Power in AC Circuits · hard · theory
The wattless component of the current in an AC circuit is:
A. $I\sin\phi$ ✓ Correct
B. $I$
C. $I\tan\phi$
D. $I\cos\phi$
Solution: This quadrature component is $90^\circ$ out of phase with the voltage and so contributes no average power.
Q8 — Power in AC Circuits · hard · theory
A low power factor in an industrial installation is undesirable because it:
A. Reduces the current drawn from the mains
B. Reduces the voltage of the supply
C. Requires a larger current for the same useful power, increasing line losses ✓ Correct
D. Increases the frequency of the supply
Solution: Since $P = VI\cos\phi$, a small $\cos\phi$ means a big $I$, and the $I^2R$ losses in the cables rise sharply.
Q9 — Power in AC Circuits · medium · theory
The power factor of an inductive load is commonly improved by:
A. Increasing the supply frequency
B. Connecting an inductor in series with the load
C. Connecting a capacitor in parallel with the load ✓ Correct
D. Increasing the resistance of the load
Solution: The leading current drawn by the capacitor partly cancels the lagging current of the inductive load.
Q10 — Power in AC Circuits · medium · numerical
An AC circuit draws $5\text{ A}$ from a $200\text{ V}$ supply with a power factor of $0.8$. The power consumed is:
A. $250\text{ W}$
B. $640\text{ W}$
C. $800\text{ W}$ ✓ Correct
D. $1000\text{ W}$
Solution: $P = V_{rms}I_{rms}\cos\phi = 200 \times 5 \times 0.8 = 800\text{ W}$.
Q11 — Power in AC Circuits · easy · numerical
A series circuit has $R = 30\,\Omega$ and impedance $50\,\Omega$. Its power factor is:
A. $0.4$
B. $0.6$ ✓ Correct
C. $0.8$
D. $1.67$
Solution: $\cos\phi = \dfrac{R}{Z} = \dfrac{30}{50} = 0.6$.
Q12 — Power in AC Circuits · easy · numerical
The average power consumed by a pure inductor connected to an AC supply is:
A. $I_{rms}^2X_L$
B. Zero ✓ Correct
C. $\dfrac{V_{rms}I_{rms}}{2}$
D. $V_{rms}I_{rms}$
Solution: The phase difference is $90^\circ$, so $\cos\phi = 0$ and the net power over a cycle vanishes.
Q13 — Power in AC Circuits · medium · numerical
An AC circuit draws $2\text{ A}$ from a $100\text{ V}$ supply with a phase angle of $60^\circ$. The power consumed is:
A. $173\text{ W}$
B. $50\text{ W}$
C. $200\text{ W}$
D. $100\text{ W}$ ✓ Correct
Solution: $P = 100 \times 2 \times \cos 60^\circ = 200 \times 0.5 = 100\text{ W}$.
Q14 — Power in AC Circuits · hard · numerical
A series LCR circuit at resonance has $R = 50\,\Omega$ across a $200\text{ V}$ RMS supply. The power consumed is:
A. $1600\text{ W}$
B. $800\text{ W}$ ✓ Correct
C. $200\text{ W}$
D. $400\text{ W}$
Solution: At resonance $P = \dfrac{V^2}{R} = \dfrac{200^2}{50} = 800\text{ W}$.
Q15 — Power in AC Circuits · easy · numerical
A resistive load draws $5\text{ A}$ from a $220\text{ V}$ supply. The power consumed is:
A. $1556\text{ W}$
B. $44\text{ W}$
C. $1100\text{ W}$ ✓ Correct
D. $550\text{ W}$
Solution: For a purely resistive load $\cos\phi = 1$, so $P = 220 \times 5 = 1100\text{ W}$.
Q16 — Power in AC Circuits · medium · numerical
An AC circuit draws $5\text{ A}$ from a $200\text{ V}$ supply. Its apparent power is:
A. $1000\text{ VA}$ ✓ Correct
B. $1414\text{ VA}$
C. $40\text{ VA}$
D. $800\text{ VA}$
Solution: Apparent power $= V_{rms}I_{rms} = 200 \times 5 = 1000\text{ VA}$, regardless of the phase angle.
Q17 — Power in AC Circuits · medium · numerical
A circuit has an apparent power of $1000\text{ VA}$ and consumes $800\text{ W}$. Its power factor is:
A. $0.8$ ✓ Correct
B. $1.25$
C. $0.6$
D. $0.2$
Solution: $\cos\phi = \dfrac{\text{true power}}{\text{apparent power}} = \dfrac{800}{1000} = 0.8$.
Q18 — Power in AC Circuits · medium · numerical
An RMS current of $3\text{ A}$ flows through a $20\,\Omega$ resistor in an AC circuit. The power dissipated is:
A. $60\text{ W}$
B. $90\text{ W}$
C. $180\text{ W}$ ✓ Correct
D. $120\text{ W}$
Solution: $P = I_{rms}^2R = 9 \times 20 = 180\text{ W}$.
Q19 — Power in AC Circuits · easy · numerical
An AC circuit draws $4\text{ A}$ from a $100\text{ V}$ supply with a power factor of $0.5$. The power consumed is:
A. $800\text{ W}$
B. $200\text{ W}$ ✓ Correct
C. $400\text{ W}$
D. $100\text{ W}$
Solution: $P = 100 \times 4 \times 0.5 = 200\text{ W}$.
Q20 — Power in AC Circuits · hard · numerical
A current of $5\text{ A}$ flows in a circuit with a phase angle of $60^\circ$. The wattless component of the current is approximately:
A. $5\text{ A}$
B. $4.33\text{ A}$ ✓ Correct
C. $2.5\text{ A}$
D. Zero
Solution: Wattless component $= I\sin\phi = 5 \times \sin 60^\circ = 5 \times 0.866 \approx 4.33\text{ A}$.
Q21 — Power in AC Circuits · easy · numerical
An RMS current of $2\text{ A}$ flows through a resistance of $25\,\Omega$. The power dissipated is:
A. $200\text{ W}$
B. $100\text{ W}$ ✓ Correct
C. $12.5\text{ W}$
D. $50\text{ W}$
Solution: $P = I^2R = 4 \times 25 = 100\text{ W}$.