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 a circuit, \(L, C\) and \(R\) are connected in series with an alternating voltage source of frequency \(f.\) The current leads the voltage by \(45^{\circ}\). The value of \(C\) will be:
1. | \(\dfrac{1}{2 \pi f \left( 2 \pi f L + R \right)}\) | 2. | \(\dfrac{1}{\pi f \left(2 \pi f L + R \right)}\) |
3. | \(\dfrac{1}{2 \pi f \left( 2 \pi f L - R \right)}\) | 4. | \(\dfrac{1}{\pi f \left(2 \pi f L - R \right)}\) |
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. \(100~\text{V}, 2~\text{A}\)
An ac source of angular frequency \(\omega\) is fed across a resistor \(r\) and a capacitor \(C\) in series. \(I\) is the current in the circuit. If the frequency of the source is changed to \(\frac{\omega}{3}\) (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency \(\omega\).
1. | \(\sqrt{\dfrac{3}{5}}\) | 2. | \(\sqrt{\dfrac{2}{5}}\) |
3. | \(\sqrt{\dfrac{1}{5}}\) | 4. | \(\sqrt{\dfrac{4}{5}}\) |
1. | \(\frac{\sqrt{5} R}{2} ,\tan^{- 1} \left(2\right)\) | 2. | \(\frac{\sqrt{5} R}{2} , \tan^{- 1} \left(\frac{1}{2}\right)\) |
3. | \(\sqrt{5} X_{C} ,\tan^{- 1} \left(2\right)\) | 4. | \(\sqrt{5} R , \tan^{- 1} \left(\frac{1}{2}\right)\) |
In a series \(LCR\) circuit, which one of the following curves represents the variation of impedance \((Z)\) with frequency \((f)\)?
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 \(\pi\). |
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 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. | \(I_0\) |