Q. No.| 1. | resistive circuit | 2. | \({LC}\) circuit |
| 3. | inductive circuit | 4. | capacitive circuit |
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. \(\frac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
2. \(-\frac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
3. \({V_mI_m}\mathrm{sin}^{2}(\omega t)\)
4. \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\)
An AC voltage source is connected to a series \(LCR\) circuit. When \(L\) is removed from the circuit, the phase difference between current and voltage is \(\frac{\pi}{3}\). If \(C\) is instead removed from the circuit, the phase difference is again \(\frac{\pi}{3}\) between current and voltage. The power factor of the circuit is:
1. \(0.5\)
2. \(1.0\)
3. \(-1.0\)
4. zero
An inductor of \(20~\text{mH}\), a capacitor of \(100~\mu \text{F}\), and a resistor of \(50~\Omega\) are connected in series across a source of emf, \(V=10 \sin (314 t)\). What is the power loss in this circuit?
1. \( 0.79 ~\text{W} \)
2. \( 0.43 ~\text{W} \)
3. \( 2.74 ~\text{W} \)
4. \( 1.13 ~\text{W}\)
The potential differences across the resistance, capacitance, and inductance are \(80~\text{V}\), \(40~\text{V}\) and \(100~\text{V}\) respectively in an \(LCR\) circuit. The power factor of this circuit is:
1. \(0.4\)
2. \(0.5\)
3. \(0.8\)
4. \(1.0\)
| 1. | over a full cycle, the capacitor \(C\) does not consume any energy from the voltage source. |
| 2. | current \(I(t)\) is in phase with voltage \(V(t)\). |
| 3. | current \(I(t)\) leads voltage \(V(t)\) by \(180^{\circ}\). |
| 4. | current \(I(t)\), lags voltage \(V(t)\) by \(90^{\circ}\). |
| 1. | \(0.67~\text{W}\) | 2. | \(0.76~\text{W}\) |
| 3. | \(0.89~\text{W}\) | 4. | \(0.51~\text{W}\) |
A resistance \(R\) draws power \(P\) when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes \(Z\), the power drawn will be:
| 1. | \(P\Big({\large\frac{R}{Z}}\Big)^2\) | 2. | \(P\sqrt{\large\frac{R}{Z}}\) |
| 3. | \(P\Big({\large\frac{R}{Z}}\Big)\) | 4. | \(P\) |
In an electrical circuit \(R,\) \(L,\) \(C\) and an \(\mathrm{AB}\) voltage source are all connected in series. When \(L\) is removed from the circuit, the phase difference between the voltage and the current in the circuit is \(\tan^{-1}\sqrt{3}\). If instead, \(C\) is removed from the circuit, the phase difference is again \(\tan^{-1}\sqrt{3}\). The power factor of the circuit is:
| 1. | \(1 / 2 \) | 2. | \(1 / \sqrt{2} \) |
| 3. | \(1 \) | 4. | \(\sqrt{3} / 2\) |
The instantaneous values of alternating current and voltages in a circuit are given as,
\(i=\frac{1}{\sqrt{2}}\sin\left ( 100\pi t \right )~\text{Ampere}\)
\(e=\frac{1}{\sqrt{2}}\sin\left ( 100\pi t+\pi /3 \right )~\text{Volt}\)
What is the average power consumed by the circuit in watts?
| 1. | \( \frac{\sqrt{3}}{4} \) | 2. | \( \frac{1}{2} \) |
| 3. | \( \frac{1}{8} \) | 4. | \( \frac{1}{4}\) |
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