\(L\), \(C\) and \(R\) represent physical quantities inductance, capacitance and resistance respectively. The combination representing the dimension of frequency will be:
1. \(LC\)
2. \((LC)^{\frac{-1}{2}}\)
3. \(\left(\frac{L}{C}\right)^{\frac{-1}{2}}\)
4. \(\frac{C}{L}\)

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 resonant circuit, the ac voltage across resistance R, inductance L and capacitance C are 5 V, 10 V and 10 V respectively. The ac voltage applied to the circuit will be 

(1) 20 V

(2) 10 V

(3) 5 V

(4) 25 V

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 the circuit shown below, the AC source has voltage \(V = 20\cos(\omega t)\) volts with \(\omega =2000\) rad/sec. The amplitude of the current is closest to:
           

1. \(2\) A

2. \(3.3\) A

3. $\mathrm{}$\(\frac{2}{\sqrt{5}}\) A

4. \(\sqrt{5}~\text{A}\) $$

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

The power factor of an ac circuit having resistance (R) and inductance (L) connected in series and an angular velocity ω is 

(1) $R/\omega L$

(2) $R/{(R^2+{\omega }^2{L}^2)}^{1/2}$

(3) $\omega L/R$

(4) $R/{(R^2-{\omega }^2{L}^2)}^{1/2}$

An inductor of inductance \(L\) and resistor of resistance \(R\) are joined in series and connected by a source of frequency \(\omega\). The power dissipated in the circuit is: