Power in AC Circuits

Practice Questions:

Question 1: easy

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An emf E = E0 cos (wt) applied to the circuit. The power consumed in the circuit is :

1. \[\frac{E_{0}^{2}}{R}\]

2. \[\frac{E_{0}^{2}}{2R}\]

3. \[\frac{E_{0}^{2}}{4R}\]

4. \[\frac{E_{0}^{2}}{8R}\]

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Question 2: difficult

An LCR series circuit with a resistance of 100 ohm is connected to an AC source of 200 V (rms) and angular frequency 300 rad/s. When only the capacitor is removed, the current lags behind the voltage by 60°. When only the inductor is removed the current leads the
voltage by 60°. The average power dissipated is :

1. 50 W

2. 100 W

3. 200 W

4. 400 W

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Question 3: moderate

In an a.c. circuit V and I are given by
V = 100 sin (100 t) volts
I = 100 sin (100t + π/3) mA
The power dissipated in the circuit is

1. \[10^{4} watt\]

2. 10 watt

3. 2.5 watt

4. 5.0 watt

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Question 4: easy

A coil has power factor of 0.707 at 60 Hz. Then its power factor at 180 Hz will be :-

1. \[\frac{1}{\sqrt{2}}\]

2. \[\frac{1}{\sqrt{5}}\]

3. \[\frac{1}{\sqrt{10}}\]

4. \[\sqrt{\frac{5}{2}}\]

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