Free Alternating Current MCQs with Answers

1. The root mean square value of an alternating current is

• A. equal to its peak value
• B. the peak value divided by the square root of 2
• C. the peak value multiplied by 2
• D. always zero

Explanation: The rms value is about 0.707 of the peak and is defined as the steady direct current that would dissipate the same power in a given resistor. Mains electricity quoted as 220 V is an rms figure, so the peak is around 311 V, which is why insulation must be rated well above the nominal value. The simple average over a full cycle is zero, which is why the rms measure is needed at all.

2. If the peak voltage of an AC supply is 311 V, its rms value is about

• A. 440 V
• B. 220 V
• C. 311 V
• D. 155 V

Explanation: Dividing 311 by the square root of 2, that is by about 1.414, gives roughly 220 V, the standard supply voltage in Pakistan. Multiplying instead gives the 440 V distractor. Half the peak, 155 V, has no physical significance here.

3. In a purely resistive AC circuit, the current and the voltage are

• A. in phase with each other
• B. 90 degrees out of phase, with current leading
• C. 90 degrees out of phase, with current lagging
• D. 180 degrees out of phase

Explanation: A resistor obeys Ohm's law at every instant, so the current peaks exactly when the voltage peaks and both pass through zero together. Phase differences appear only when capacitance or inductance is present. Because they are in phase, all the power in a resistive circuit is dissipated as heat.

4. In a purely capacitive AC circuit, the current

• A. lags the voltage by 90 degrees
• B. leads the voltage by 90 degrees
• C. is in phase with the voltage
• D. is zero

Explanation: A capacitor must charge before a voltage can appear across it, so the current is greatest when the voltage is momentarily zero and falls to zero when the voltage is at its peak, putting the current a quarter cycle ahead. The mnemonic ICE captures this: in a capacitor, I comes before E. An inductor does the reverse, with the current lagging.

5. The capacitive reactance of a capacitor

• A. increases as the frequency increases
• B. decreases as the frequency increases
• C. is independent of frequency
• D. is the same as resistance

Explanation: Reactance is one over 2 pi f C, so a capacitor passes high frequencies readily and blocks direct current entirely, since at zero frequency the reactance is infinite. This is why capacitors are used to couple audio signals while blocking any DC bias. An inductor behaves in the opposite way, opposing high frequencies most.

6. The inductive reactance of a coil is given by

• A. 2 pi f L
• B. 1 divided by 2 pi f L
• C. L divided by 2 pi f
• D. 2 pi f divided by L

Explanation: Reactance rises in proportion to frequency, so a coil that passes direct current almost freely offers a large opposition at high frequency. That is why an inductor is called a choke and is used to smooth or to block radio frequency signals. It has units of ohms but dissipates no power, since the current and voltage are 90 degrees out of phase.

7. The average power dissipated in a purely inductive or purely capacitive AC circuit over a complete cycle is

• A. maximum
• B. zero, because energy is stored and returned each quarter cycle
• C. equal to VI
• D. half of VI

Explanation: With a 90 degree phase difference the power is positive for one quarter cycle and equally negative for the next, so the net energy transfer over a full cycle is zero: the component stores energy in its field and returns it to the source. Only resistance actually dissipates energy as heat. This is why the power factor, cos of the phase angle, is zero for a pure reactance.

8. In a series RLC circuit at resonance

• A. the impedance is maximum and the current minimum
• B. the impedance is minimum and equal to the resistance, so the current is maximum
• C. the current is zero
• D. the capacitor and inductor can be removed without effect

Explanation: At resonance the inductive and capacitive reactances are equal and cancel, leaving only the resistance to oppose the current, so the current peaks sharply. The resonant frequency is 1 over 2 pi times the square root of LC. Tuning a radio means adjusting a capacitor until the resonant frequency matches the station wanted.

9. The power factor of an AC circuit is defined as

• A. the ratio of peak to rms current
• B. the cosine of the phase angle between current and voltage
• C. the ratio of frequency to reactance
• D. the product of voltage and current

Explanation: True power is V times I times cos theta, so the power factor measures how much of the apparent power is actually being converted to useful work. It is 1 for a purely resistive circuit and zero for a pure reactance. Industrial users correct a poor power factor with capacitors, because a low value means large currents and heavy cable losses for the same useful power.

10. The frequency of the alternating mains supply in Pakistan is

• A. 50 Hz
• B. 60 Hz
• C. 100 Hz
• D. 220 Hz

Explanation: Pakistan, like most of Asia and Europe, uses 50 Hz at 220 V, while North America uses 60 Hz at 110 V. A frequency of 50 Hz means the current reverses direction 100 times each second, since there are two reversals per cycle. The figure 220 belongs to the voltage rather than the frequency.