Free Phase of 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. 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.

4. Alternating current cannot be measured with a moving coil galvanometer directly because

• A. the current is too large
• B. the deflection reverses every half cycle and the pointer cannot follow, so it averages to zero
• C. the galvanometer has no coil
• D. AC does not flow through a galvanometer

Explanation: The torque reverses with the current, and at 50 Hz the inertia of the pointer prevents it from following, so it simply sits at zero. Measuring AC therefore requires either a rectifier ahead of the meter or an instrument such as a hot wire ammeter that responds to the heating effect, which does not depend on direction. This is why hot wire meters read rms values directly.

5. The peak value of an alternating current whose rms value is 10 A is about

• A. 7.07 A
• B. 14.14 A
• C. 10 A
• D. 20 A

Explanation: The peak is the rms multiplied by the square root of 2, so 10 times 1.414 gives 14.14 A. Dividing instead gives 7.07 A, which would be the rms if 10 A were the peak. Keeping track of which value a question quotes is the whole difficulty in these problems.

6. A phase difference of 90 degrees is equal to:

• A. pi radians
• B. pi/2 radians
• C. 2 pi radians
• D. pi/4 radians

Explanation: A complete cycle is 360 degrees or 2 pi radians, so 90 degrees is a quarter of a cycle, that is pi over 2 radians. This is the phase difference between current and voltage in a purely capacitive or purely inductive AC circuit, which is why no net power is dissipated in either. The Greek letter did not print cleanly in the original paper.