Q. No.An inductor \((L)\) and resistance \((R)\) are connected in series with an AC source. The phase difference between voltage \((V)\) and current \((i)\) is \(45^{\circ}.\)
If the phase difference between \(V\) and \(i\) remains the same, then the capacitive reactance and impedance of the \(LCR\) circuit will be:
1. \(2R, R\sqrt{2}\)
2. \(R, R\sqrt{2}\)
3. \(R, R\)
4. \(2R, R\sqrt{3}\)
1. \(2R, R\sqrt{2}\)
2. \(R, R\sqrt{2}\)
3. \(R, R\)
4. \(2R, R\sqrt{3}\)
A series AC circuit has a resistance of \(4~\Omega\) and an inductor of reactance \(3~\Omega\). The impedance of the circuit is \(z_1\). Now when a capacitor of reactance \(6~\Omega\) is connected in series with the above combination, the impedance becomes \(z_2\). Then \(\frac{z_1}{z_2}\) will be:
1. \(1:1\)
2. \(5:4\)
3. \(4:5\)
4. \(2:1\)
Which of the following would change the potential difference measured by the voltmeter in the system above?
| (a) | use more turns of wire in the coil. |
| (b) | use thicker wire. |
| (c) | change the speed of rotation. |
| 1. | (c) only |
| 2. | (a), (b) and (c) |
| 3. | (a) and (b) only |
| 4. | (a) and (c) only |
1. \(\frac{E^2_0}{\sqrt{2}R}\)
2. \(\frac{E^2_0}{4R}\)
3. \(\frac{E^2_0}{2R}\)
4. \(\frac{E^2_0}{8R}\)
1. \(300\) V, \(15\) A
2. \(450\) V, \(15\) A
3. \(450\) V, \(13.5\) A
4. \(600\) V, \(15\) A
The core of a transformer is laminated because:
| 1. | Energy losses due to eddy currents may be minimized |
| 2. | The weight of the transformer may be reduced |
| 3. | Rusting of the core may be prevented |
| 4. | Ratio of voltage in primary and secondary may be increased |
| 1. | \(\frac{\varepsilon^{2} R}{\left[R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}\right]}\) | 2. | \(\frac{\varepsilon^{2} \sqrt{R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}}}{R}\) |
| 3. | \(\frac{\varepsilon^{2}\left[R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}\right]}{R}\) | 4. | \(\frac{\varepsilon^{2}R}{\sqrt{R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}}}\) |
A coil of inductive reactance of \(31~\Omega\) has a resistance of \(8~\Omega\). It is placed in series with a condenser of capacitive reactance \(25~\Omega\). The combination is connected to an AC source of \(110\) V. The power factor of the circuit is:
1. \(0.56\)
2. \(0.64\)
3. \(0.80\)
4. \(0.33\)
1. \(3.6\) A
2. \(2.8\) A
3. \(2.5\) A
4. \(5.0\) A
| 1. | When the capacitor is air-filled. |
| 2. | When the capacitor is mica filled. |
If the current through the resistor is \(I\) and the voltage across the capacitor is \(V\), then:
1. \(V_a < V_b\)
2. \(V_a > V_b\)
3. \(i_a > i_b\)
4. \(V_a = V_b\)
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