The value of the quality factor is:
1. $\frac{\omega L}{R}$

2. $\frac{\omega }{RC}$

3. $\sqrt{LC}$

4. L/R

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 \(C\) is:
1. \(\frac{1}{2 \pi f(2 \pi f L-R)}\)
2. \(\frac{1}{2\pi f(2 \pi f L+R)}\)
3. \(\frac{1}{ \pi f(2 \pi f L-R)}\)
4. \(\frac{1}{\pi f(2 \pi f L+R)}\)

Turn ratio of a step-up transformer is \(1: 25\). If current in load coil is \(2~\text{A}\), then the current in primary coil will be:

A coil of \(40\) H inductance is connected in series with a resistance of \(8~\Omega\) and the combination is joined to the terminals of a \(2~\text{V}\) battery. The time constant of the circuit is:
1. \(1/5~\text{s}\)
2. \(40~\text{s}\)
3. \(20~\text{s}\)
4. \(5~\text{s}\)

For a series \(\mathrm{LCR}\) circuit, the power loss at resonance is:
1. \(\frac{V^2}{\left[\omega L-\frac{1}{\omega C}\right]}\)

2. \( \mathrm{I}^2 \mathrm{~L} \omega \)

3. \(I^2 R\)

4. \( \frac{\mathrm{V}^2}{\mathrm{C} \omega} \)

An inductor of inductance \(L\), a capacitor of capacitance \(C\) and a resistor of resistance \(R\) are connected in series to an AC source of potential difference \(V\) volts as shown in Figure. The potential difference across \(L\), \(C\) and \(R\) is \(40~\text{V}\), \(10~\text{V}\) and \(40~\text{V}\), respectively. The amplitude of the current flowing through the \(LCR\) series circuit is \(10\sqrt{2}~\text{A}\). The impedance of the circuit will be:

A series \(LCR\) circuit containing \(5.0~\text{H}\) inductor, \(80~\mu \text{F}\) capacitor and \(40~\Omega\)$\mathrm{}$ resistor is connected to \(230~\text{V}\) variable frequency AC source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be: