A series LCR circuit containing \(5.0~\text{H}\) inductor, \(80~\mu \text{F}\) capacitor and \(40~\Omega\) 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:
1. | \(46~\text{rad/s}~\text{and}~54~\text{rad/s}\) |
2. | \(42~\text{rad/s}~\text{and}~58~\text{rad/s}\) |
3. | \(25~\text{rad/s}~\text{and}~75~\text{rad/s}\) |
4. | \(50~\text{rad/s}~\text{and}~25~\text{rad/s}\) |
1. | When the DC source is connected to the capacitor, the lamp will not glow in a steady-state condition. |
2. | When the AC source is connected to the capacitor and the capacitance of the capacitor is reduced, the lamp will glow less brightly. |
3. | When the DC source is connected to the capacitor and the capacitance of the capacitor is reduced, the lamp will glow less brightly. |
4. | Both (1) and (2). |
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:
1. | \(25~\text{A}\) | 2. | \(50~\text{A}\) |
3. | \(0.25~\text{A}\) | 4. | \(0.5~\text{A}\) |
1. | \(2.0~\text{A}\) | 2. | \(4.0~\text{A}\) |
3. | \(8.0~\text{A}\) | 4. | \(20/\sqrt{13}~\text{A}\) |
1. | \(\dfrac{V_{0}}{\sqrt{3}}\) | 2. | \(V_{0}\) |
3. | \(\dfrac{V_{0}}{\sqrt{2}}\) | 4. | \(\dfrac{V_{0}}{2}\) |
1. | \( \frac{\sqrt{3}}{4} \) | 2. | \( \frac{1}{2} \) |
3. | \( \frac{1}{8} \) | 4. | \( \frac{1}{4}\) |
1. | voltage across the capacitor lags behind the current. |
2. | voltage across the inductor leads the current. |
3. | voltage across \(R\) is in phase with the current. |
4. | all of the above. |
Assertion (A): | If the frequency of the applied AC is doubled, then the power factor of a series \(R\text-L\) circuit decreases. |
Reason (R): | \(R\text-L\) circuit is given by \(\cos \theta=\frac{2 R}{\sqrt{R^{2}+\omega^{2} {L}^{2}}}.\) | Power factor of series
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
Assertion (A): | Large-scale transmission and distribution of electric energy over long distances are done by stepping the voltage up by a transformer. |
Reason (R): | This cuts down the loss of energy due to eddy currents. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
Assertion (A): | If the terminals of the primary of a transformer are connected across a battery then no emf is induced across the secondary in a steady state. |
Reason (R): | The battery provides a steady current, so there is no change in flux linked with the secondary. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |