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. | \(\sqrt{3} / 2\) |
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. \( 1.13 ~\text{W}\)
An AC source rated \(100~\text{V}\) (rms) supplies a current of \(10~\text{A}\) (rms) to a circuit. The average power delivered by the source:
(a) | must be \(1000~\text{W}\). |
(b) | may be \(1000~\text{W}\). |
(c) | may be greater than \(1000~\text{W}\). |
(d) | may be less than \(1000~\text{W}\). |
1. | (a) only |
2. | (b), (c) |
3. | (b), (d) |
4. | (a), (d) |
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. \(\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
2. \(-\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
3. \({V_mI_m}\mathrm{sin}^{2}(\omega t)\)
4. \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\)
1. | \( \frac{\sqrt{3}}{4} \) | 2. | \( \frac{1}{2} \) |
3. | \( \frac{1}{8} \) | 4. | \( \frac{1}{4}\) |
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. \( \frac{\mathrm{V}^2}{\mathrm{C} \omega} \)