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. | \(50~\text{rad/s}~\text{and}~25~\text{rad/s}\) |
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:
1. | \(4~\Omega\) | 2. | \(5~\Omega\) |
3. | \(4\sqrt{2}~\Omega\) | 4. | \(\dfrac{5}{\sqrt{2}}~\Omega\) |
A light bulb and an inductor coil are connected to an AC source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb:
1. | decreases |
2. | remains unchanged |
3. | will fluctuate |
4. | increases |
1. | \(1 / \sqrt{2}\) times the rms value of the AC source. |
2. | the value of voltage supplied to the circuit. |
3. | the rms value of the AC source. |
4. | \(\sqrt{2}\) times the rms value of the AC source. |
1. | \(\nu=100 ~\text{Hz} ; ~\nu_0=\dfrac{100}{\pi} ~\text{Hz}\) |
2. | \(\nu_0=\nu=50~\text{Hz}\) |
3. | \(\nu_0=\nu=\dfrac{50}{\pi} ~\text{Hz}\) |
4. | \(\nu_{0}=\dfrac{50}{\pi}~ \text{Hz}, \nu=50 ~\text{Hz}\) |
An AC source given by \(V=V_m\sin\omega t\) is connected to a pure inductor \(L\) in a circuit and \(I_m\) is the peak value of the AC current. The instantaneous power supplied to the inductor is:
1. \(\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
2. \(-\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
3. \({V_mI_m}\mathrm{sin}^{2}(\omega t)\)
4. \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\)
Statement I: | In an AC circuit, the current through a capacitor leads the voltage across it. |
Statement II: | \(\pi.\) | In AC circuits containing pure capacitance only, the phase difference between the current and the voltage is
1. | Both Statement I and Statement II are correct. |
2. | Both Statement I and Statement II are incorrect. |
3. | Statement I is correct but Statement II is incorrect. |
4. | Statement I is incorrect but Statement II is correct. |