\(L\), \(C\) 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 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:
1. \(\dfrac{\left( R^{2} +\omega^{2} L^{2} \right)}{V}\)

2. \(\dfrac{V^{2} R}{\left(R^{2} + \omega^{2} L^{2} \right)}\)

3. \(\dfrac{V}{\left(R^{2} + \omega^{2} L^{2}\right)}\)

4. \(\dfrac{\sqrt{R^{2} + \omega^{2} L^{2}}}{V^{2}}\)

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