MCQ on Power of Alternating Current: Introduction & Explanation

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The power of alternating current is defined as the ratio of true power flowing through the circuit to the apparent power present in the circuit. The power is the product of voltage and time. The power of the alternating current cannot be calculated because in an AC circuit, the EMF and current change continuously with respect to time. Thus, to obtain the average power of an alternating current circuit, we need to calculate the instantaneous power of the circuit.

The formula for average power in an AC circuit is given by,

$P_{av} = \int\limits_0^T VI\ dt/ \int\limits_0^T dt$

Power of Alternating Current MCQs

Ques 1. The direction of current in an AC circuit is:

Always positive
Always negative
Either positive or negative
Changes constantly

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Ans. (d). Changes constantly

Explanation: The direction of current in an AC circuit changes constantly. The voltage also reverses periodically in an AC circuit.

Ques 2. The average power supplied to an inductor over one complete alternating current cycle is:

0
IV²
VI²
IR²

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Ans. (a). 0

Explanation: For a pure inductor circuit, ϕ = 90° (∵ current lags the voltage by 90° in the pure inductive circuit)

Cos ϕ = Cos 90° = 0

P = V_rmsI_rms 0

P = 0 W

Ques 3. In an AC circuit, V = 100 sint V and I = 100 sin (100t + $\sqrt 2$/3) A, then average power loss will be:

10⁴ W
2.5 kW
10 W
100 W

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Ans. (b). 2.5 kW

Explanation: Here, potential difference (V) = 100 sint V and I = 100 sin (100t + $\sqrt 2$/3) A

So, peak voltage (E_o) = 100, peak current (I_o) = 100 and phase difference (θ) = $\sqrt 2$/3

The average power loss in an AC circuit is given by;

P = V_rmsI_rmsCosθ

P = V_o/$\sqrt 2$ I_o/$\sqrt 2$ Cosθ

P = 100/$\sqrt 2$2 100/$\sqrt 2$2 cos $\sqrt 2$/3

P = 2.5 x 10³ W

P = 2.5 kW

Ques 4. In a series LCR circuit, alternating emf (v) and current are given by v = vo sin t, i = io sin (t + ????/3). The average power dissipated in the circuit over a cycle of AC is:

v_oi_o/2
v_oi_o/4
3/2 v_oi_o
Zero

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Ans. (b). v_oi_o/4

Explanation: v = v_o sin (t)

i = i_o sin (t + $\sqrt 2$/3)

Phase difference (θ) = $\sqrt 2$/3

Peak current (I) = i_o

Peak voltage (V) = v_o

rms current (I_rms) = I/$\sqrt 2$ = i_o/$\sqrt 2$

rms voltage (V_rms) = V/$\sqrt 2$ = vo/$\sqrt 2$

P_avg = V_rmsI_rmsCosθ

Average power (P_avg) = v_o/$\sqrt 2$ i_o/$\sqrt 2$ Cos$\sqrt 2$/3

P_avg = v_oi_o/2 x ½ = v_oi_o/4

Ques 5. A series LCR circuit with R = 40, L = 30 H and C = 25F is connected to a 200 V AC supply. At resonance what will be the average power transferred to the circuit in one complete cycle?

1000 W
2000 W
3000 W
4000 W

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Ans. (a). 1000 W

Explanation: Given, R = 40 $\Omega$, L = 30 H, C = 25$\mu$F and E_rms = 200 V

At resonance, X_L = X_C

Z = $\sqrt R ^2$ + $\sqrt {(X_L - X_C)^2}$ = $\sqrt 40 ^2$ = 40

Average power dissipated per cycle is,

P_av = E²_rms / Z = (200)2/40 = 1000 W

Ques 6. A coil of inductive reactance 31 has a resistance of 8. It is placed in series with a condenser of capacitance reactance 25. The combination is connected to an AC source of 110 V. The power factor of the circuit is:

0.4
0.64
0.8
1.6

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Ans. (c). 0.8

Explanation: R = 8$\Omega$, XC = 25, XL = 31 and V = 110 V

Z = $\sqrt R ^2$ + $\sqrt {(X_L - X_C)^2}$

Z = $\sqrt 8 ^2$ + $\sqrt {(31 - 25)^2}$ = $\sqrt {(64+36)}$

Z = 10$\Omega$

The power factor (P) of a series LCR-circuit is given by,

Cos ϕ = R/Z

Cos ϕ = 8/10 = 0.8

Ques 7. Average power in an LCR circuit depends upon:

Current
Current, emf, and phase difference
Emf
Phase difference

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Ans. (b). Current, emf, and phase difference

Explanation: The average power dissipated in an LCR circuit is given by;

P_avg = V_rmsI_rmsCosθ

Thus, the average power depends upon current, emf, and phase difference.

Ques 8. Power loss in an AC circuit is measured by:

Power factor
Mean current
Impedance
None of these

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Ans. (a). Power factor

Explanation: The power factor in an AC circuit is defined as the ratio of the actual power used by the circuit to the apparent power of the circuit. It is the amount by which power delivered in the circuit is less than the theoretical power of the circuit. Hence, it is a measure of loss of power in an AC circuit.

Ques 9. Which of the following quantities changes in an alternating current?

Direction
Magnitude
Magnitude and direction both
None of the above

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Ans. (c). Magnitude and direction both

Explanation: In an alternating current, both the direction and the magnitude vary. The waveform of an AC power circuit is usually a sine wave. The sine wave oscillates periodically between positive and negative directions and leads to the most efficient transmission of energy.

Ques 10. The frequency of AC mains in India is:

30 Hz
50 Hz
60 Hz
120 Hz

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Ans. (b). 50 Hz

Explanation: In most European countries, the frequency of AC mains is 50 Hz. In the USA, it is 60 Hz.

Ques 11. The AC produced in India changes its direction in every:

1/100 second
100 second
50 second
None of the above

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Ans. (a). 1/100 second

Explanation: The frequency of AC voltage in India is 50 Hz. It means 50 waves are produced in 1 second. In a single wave, the direction changes 2 times. Thus, in 50 waves direction will be changed, 50 2 = 100 times.

This indicates that the direction is changed 100 times in 1 second. Thus, the direction is changed every 1/100 second.

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MCQ on Power of Alternating Current: Introduction & Explanation

Power of Alternating Current MCQs

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Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

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MCQ on Power of Alternating Current: Introduction & Explanation

Power of Alternating Current MCQs

CBSE CLASS XII Related Questions

5.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

5.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?