In an ac circuit, the current is given by $i=5\sin \left(100t-\frac{{\displaystyle \pi }}{{\displaystyle 2}}\right)$ and the ac potential is V = 200 sin(100t) volt. Then the power consumption is :

1. 20 watts

2. 40 watts

3. 1000 watts

4. 0 watt

A resistance of \(300~\Omega\) and an inductance of \(\frac{1}{\pi}\) henry are connected in series to an AC voltage of \(20\) volts and a \(200\) Hz frequency. The phase angle between the voltage and current will be:

In a LCR circuit having L = 8.0 henry, C = 0.5 μF and R = 100 ohm in series. The resonance frequency in radian per second is 

1. 600 radian/second

2. 600 Hz

3. 500 radian/second

4. 500 Hz

The phase difference between the current and voltage of LCR circuit in series combination at resonance is 

1. 0

2. π/2

3. π

4. –π

In a series LCR circuit, resistance R = 10Ω and the impedance Z = 20Ω. The phase difference between the current and the voltage is 

1. 30°

2. 45°

3. 60°

4. 90°

In an ac circuit the reactance of a coil is \(\sqrt{3}\) times its resistance, the phase difference between the voltage across the coil to the current through the coil will be:
1. \( \pi / 3 \)
2. \( \pi / 2 \)
3. \( \pi / 4 \)
4. \( \pi / 6\)

The capacity of a pure capacitor is 1 farad. In dc circuits, its effective resistance will be 

1. Zero

2. Infinite

3. 1 ohm

4. 1/2 ohm

In an \(LCR\) circuit, the potential difference between the terminals of the inductance is \(60\) V, between the terminals of the capacitor is \(30\) V and that between the terminals of the resistance is \(40\) V. The supply voltage will be equal to:

1. \(50\) V

2. \(70\) V

3. \(130\) V

4. \(10\) V

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An e.m.f. $E=E_0\cos \left(\omega t\right)$ 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. $\frac{E_0^2}{8R}$