In an ac circuit, a resistance of \(R\) ohm is connected in series with an inductance \(L\). If the phase angle between voltage and current is \(45^{\circ}\), the value of inductive reactance will be:

1.	\(\frac{R}{4}\)
2.	\(\frac{R}{2}\)
3.	\(R\)
4.	Cannot be found with the given data

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

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

In a circuit, \(L, C\) and \(R\) are connected in series with an alternating voltage source of frequency \(f.\) The current leads the voltage by \(45^{\circ}\). The value of \(C\) will be:
1. \(\frac{1}{2 \pi f \left( 2 \pi f L + R \right)}\)

2. \(\frac{1}{\pi f \left(2 \pi f L + R \right)}\)

3. \(\frac{1}{2 \pi f \left( 2 \pi f L - R \right)}\)

4. \(\frac{1}{\pi f \left(2 \pi f L - R \right)}\)