An inductor of inductance \(L\) and resistor of resistance \(R\) are joined in series and connected by a source of frequency \(\omega\). The power dissipated in the circuit is:
1. | \(\dfrac{\left( R^{2} +\omega^{2} L^{2} \right)}{V}\) | 2. | \(\dfrac{V^{2} R}{\left(R^{2} + \omega^{2} L^{2} \right)}\) |
3. | \(\dfrac{V}{\left(R^{2} + \omega^{2} L^{2}\right)}\) | 4. | \(\dfrac{\sqrt{R^{2} + \omega^{2} L^{2}}}{V^{2}}\) |
In an \(LCR\) circuit, the potential difference between the terminals of the inductance is \(60\) V, between the terminals of the capacitor is \(30\) V and that between the terminals of the resistance is \(40\) V. The supply voltage will be equal to:
1. \(50\) V
2. \(70\) V
3. \(130\) V
4. \(10\) V
In the circuit shown below, what will be the readings of the voltmeter and ammeter?
1. \(800~\text{V}, 2~\text{A}\)
2. \(300~\text{V}, 2~\text{A}\)
3. \(220~\text{V}, 2.2~\text{A}\)
4. \(100~\text{V}, 2~\text{A}\)
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 \(\pi\). |
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. | \(I_0 \over 2\) |
3. | \(2I_0 \over \pi\) | 4. | \(I_0\) |
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. | 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 |
1. | \(\frac{R}{4}\) |
2. | \(\frac{R}{2}\) |
3. | \(R\) |
4. | Cannot be found with the given data |