Q. No.In an electrical circuit \(R,\) \(L,\) \(C\) and an AC 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. | \(\dfrac{1}{2} \) | 2. | \(\dfrac{1}{\sqrt{2}}\) |
| 3. | \(1 \) | 4. | \(\dfrac{\sqrt{3}}{2}\) |
| 1. | \(100~\text{mA}\) | 2. | \(200~\text{mA}\) |
| 3. | \(20~\text{mA}\) | 4. | \(10~\text{mA}\) |
1. \(300~\text V,~15~\text A\)
2. \(450~\text V,~15~\text A\)
3. \(450~\text V,~13.5~\text A\)
4. \(600~\text V,~15~\text A\)
\(i=\frac{1}{\sqrt{2}}\sin\left(100\pi t \right )~\text{Ampere}\)
\(e=\frac{1}{\sqrt{2}}\sin\left(100\pi t+\pi /3 \right)~\text{Volt}\)
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. | \( \frac{1}{4}\) |
| 1. | \(\dfrac{V_{0}}{\sqrt{3}}\) | 2. | \(V_{0}\) |
| 3. | \(\dfrac{V_{0}}{\sqrt{2}}\) | 4. | \(\dfrac{V_{0}}{2}\) |
An AC voltage is applied to a resistance R and an inductor L in series. If R and the inductive reactance are both equal to 3 , the phase difference between the applied voltage and the current in the circuit is:
1.
2.
3. zero
4.
A series \(RC\) circuit is connected to an alternating voltage source. Consider two situations:
(1) When the capacitor is air-filled.
(2) When the capacitor is mica filled.
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. \(V_a = V_b\)
| 1. | \(2.0~\text{A}\) | 2. | \(4.0~\text{A}\) |
| 3. | \(8.0~\text{A}\) | 4. | \(20/\sqrt{13}~\text{A}\) |
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. | \(P\) |
| 1. | \(20~\text{V}\) and \(2.0~\text{mA}\) |
| 2. | \(10~\text{V}\) and \(0.5~\text{mA}\) |
| 3. | zero and therefore no current |
| 4. | \(20~\text{V}\) and \(0.5~\text{mA}\) |
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