Q. No.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
1. \(50\) 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. | \(I_0\) |
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. | \(R=1 ~\text{k}\Omega, L=1~\text{H}\) |
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