Q. No.In the diagram, two sinusoidal voltages of the same frequency are shown. What is the frequency and the phase relationship between the voltages?
Frequency in Hz
Phase lead of \(N\) over \(M\) in radians
1.
\(0.4\)
\(-\pi/4\)
2.
\(2.5\)
\(-\pi/2\)
3.
\(2.5\)
\(+\pi/2\)
4.
\(2.5\)
\(-\pi/4\)
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)
| 1. | \(\frac{1}{100}~\text{sec}\) | 2. | \(\frac{1}{200}~\text{sec}\) |
| 3. | \(\frac{1}{300}~\text{sec}\) | 4. | \(\frac{1}{400}~\text{sec}\) |
The potential differences across the resistance, capacitance and inductance are \(80\) V, \(40\) V and \(100\) V respectively in an \(LCR\) circuit.
What is the power factor of this circuit?
1. \(0.4\)
2. \(0.5\)
3. \(0.8\)
4. \(1.0\)
| 1. | Frequency of the AC source is decreased |
| 2. | The number of turns in the coil is reduced |
| 3. | A capacitance of reactance \(X_C = X_L\) is included in the same circuit |
| 4. | An iron rod is inserted in the coil |
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 \(3~ \Omega, \) then the phase difference between the applied voltage and the current in the circuit will be:
| 1. | \( \pi / 4\) | 2. | \( \pi / 2\) |
| 3. | zero | 4. | \( \pi / 6\) |
When an AC source of emf \(e = E_0 \sin (100t)\) is connected across a circuit, the phase difference between the emf \(e\) and the current \(i\) in the circuit is observed to be \(\frac{\pi}{4}\) as shown in the diagram. If the circuit consists only of \(RC\) or \(LC\) in series, then what is the relationship between the two elements?
| 1. | \(R=1~\text{k} \Omega, C=10 ~\mu \text{F}\) |
| 2. | \(R=1~\text{k}\Omega, C=1~\mu \text{F}\) |
| 3. | \(R=1 ~\text{k}\Omega, L=10 ~\text{H}\) |
| 4. | \(R=1 ~\text{k}\Omega, L=1~\text{H}\) |
The output current versus time curve of a rectifier is shown in the figure. The average value of the output current in this case will be:
1. \(0\)
2. \(\dfrac{I_0}{2}\)
3. \(\dfrac{2I_0 }{ \pi}\)
4. \(I_0\)
A constant voltage at different frequencies is applied across a capacitance \(C\) as shown in the figure.
Which of the following graphs accurately illustrates how current varies with frequency?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The variation of the instantaneous current \((I)\) and the instantaneous emf \((E)\) in a circuit are shown in the figure. Which of the following statements is correct?
| 1. | The voltage lags behind the current by \(\frac{\pi}{2}\). |
| 2. | The voltage leads the current by \(\frac{\pi}{2}\). |
| 3. | The voltage and the current are in phase. |
| 4. | The voltage leads the current by \(\pi\). |
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