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Alternating Current and Generators Quiz Set 1

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Alternating Current and Generators Quiz Set 1

Prompt

Answer the following multiple-choice questions.

Questions

1. Household Mains Voltage

A household electrical socket is labelled 240 V. Which statement is correct?

A. The voltage is a steady direct current of 240 V.
B. The maximum peak voltage of the supply is 240 V.
C. The peak voltage of the supply is approximately 340 V.
D. The mean voltage of the supply over one full cycle is 240 V.

2. Flux Linkage and Induced emf

Which statement accurately describes the relationship between magnetic flux linkage through the coil and induced emf in an AC generator?

A. The induced emf is at its maximum when the magnetic flux linkage is at its maximum.
B. The induced emf is zero when the magnetic flux linkage crosses zero.
C. The induced emf is zero when the magnetic flux linkage is at its maximum.
D. The induced emf and magnetic flux linkage are perfectly in phase.

3. Mean Current and Average Power

A student claims that because the mean current of a sinusoidal alternating current over one full cycle is zero, the average power dissipated in a resistor must also be zero. Why is this claim incorrect?

A. The mean current is actually equal to the rms current.
B. Power depends on the square of the current, so negative currents still produce positive heating.
C. The resistor stores the current during the negative half-cycle.
D. The average power is calculated using only the positive peak values.

4. Ideal Step-Up Transformer

An ideal step-up transformer is used in a power transmission grid. Which statement is correct?

A. It increases the voltage, increases the current, and increases total ideal power.
B. It increases the voltage, decreases the current, and conserves total ideal power.
C. It decreases the voltage, increases the current, and conserves total ideal power.
D. It decreases the voltage, decreases the current, and decreases total ideal power.

5. Cable Heating Loss

In high-voltage power transmission, what happens to the power lost to cable heating if the transmission current is doubled?

A. The power loss doubles.
B. The power loss halves.
C. The power loss quadruples.
D. The power loss remains unchanged.

6. Full-Wave Rectifier Output

Which statement best describes the output of a full-wave rectifier without any smoothing capacitor?

A. A pure, steady direct current identical to that of a battery.
B. An alternating current that reverses direction at twice the original frequency.
C. A pulsating direct current that flows in one direction but varies in magnitude.
D. Widely spaced pulses of current with zero voltage between each pulse.

7. Generator Frequency

A student wants to increase the frequency of the alternating current produced by a simple AC generator. Which change must be made?

A. Increase the magnetic flux density B.
B. Increase the number of turns N.
C. Increase the cross-sectional area A.
D. Increase the rotational speed \omega.

Answer

1. C

240 V for household mains refers to the rms voltage. For a sinusoidal supply:

So the peak voltage is approximately:

2. C

In an AC generator:

The induced emf depends on the rate of change of flux linkage, not the flux linkage itself.

So:

  • when the flux linkage is at a maximum or minimum, its gradient is zero
  • the induced emf is zero at those instants
  • the induced emf and flux linkage are out of phase

3. B

Power dissipated in a resistor depends on:

So both positive and negative current values give positive heating. Mean current over a full cycle may be zero, but average power is not zero.

4. B

For an ideal step-up transformer:

  • voltage increases
  • current decreases
  • total ideal power is conserved

So:

5. C

Transmission-cable heating loss is:

If the current doubles, the loss becomes four times larger.

6. C

A full-wave rectifier makes the current through the load stay in one direction, but the magnitude still varies with time. The output is pulsating DC unless smoothing is added.

7. D

For a simple rotating-coil AC generator:

So increasing the rotational speed increases the frequency.

By contrast, increasing B, N, or A increases the peak induced emf, but does not change the frequency.

Marking Notes

  • For Question 1, accept the explicit statement that 240 V is the rms value.
  • For Question 2, accept any equivalent explanation using slope or rate of change of flux linkage.
  • For Question 3, accept answers that state average power depends on the square of current or on rms current.
  • For Question 6, accept equivalent wording such as unidirectional but varying output.

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