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. \( 1.13 ~\text{W}\)
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. | \(\sqrt{3} / 2\) |
1. | \(100~\text{mA}\) | 2. | \(200~\text{mA}\) |
3. | \(20~\text{mA}\) | 4. | \(10~\text{mA}\) |
A transformer is used to light a \(100~\text{W}\) and \(110~\text{V}\) lamp from a \(220~\text{V}\) main. If the main current is \(0.5~\text{A}\), the efficiency of the transformer is approximately:
1. \(30\%\)
2. \(50\%\)
3. \(90\%\)
4. \(10\%\)
1. | \(14~\text{A}\) | about2. | \(28~\text{A}\) | about
3. | \(20~\text{A}\) | about4. | cannot say |
The variation of EMF with time for four types of generators is shown in the figures. Which amongst them can be called AC voltage?
(a) | (b) |
(c) | (d) |
1. | (a) and (d) |
2. | (a), (b), (c), and (d) |
3. | (a) and (b) |
4. | only (a) |
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. \( \frac{\mathrm{V}^2}{\mathrm{C} \omega} \)
A light bulb is rated at \(100~\text{W}\) for a \(220~\text{V}\) AC supply. The RMS current through the bulb is:
1. \(0.243\) A
2. \(0.454\) A
3. \(0.222\) A
4. \(0.312\) A
A \(15.0~\mathrm{\mu F}\) capacitor is connected to a \(220~\mathrm{V}\), \(50~\mathrm{Hz}\) source. If the frequency is doubled, what happens to the capacitive reactance and the current?
1. | the capacitive reactance is halved and the current is doubled. |
2. | the capacitive reactance is doubled and the current is halved. |
3. | the capacitive reactance remains the same and the current is doubled. |
4. | the current remains the same and the capacitive reactance is halved. |