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. $\frac{2}{\sqrt{5}}$ 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:

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:

For the series LCR circuit shown in the figure, what is the resonance frequency and the amplitude of the current at the resonating frequency ?

1. 2500 rad/s and $5\sqrt{2}A$

2. 2500 rad/s and 5A

3. 2500 rad/s and $\frac{5}{\sqrt{2}}A$

4. 25 rad/s and $5\sqrt{2}A$