Q. No.\(L\), \(C\) and \(R\) represent physical quantities inductance, capacitance and resistance respectively. The combination representing the dimension of frequency will be:
1. \(LC\)
2. \((LC)^{\frac{-1}{2}}\)
3. \(\left(\frac{L}{C}\right)^{\frac{-1}{2}}\)
4. \(\frac{C}{L}\)
| 1. | \(\frac{R}{4}\) |
| 2. | \(\frac{R}{2}\) |
| 3. | \(R\) |
| 4. | Cannot be found with the given data |
In the circuit shown below, the AC source has voltage \(V = 20\cos(\omega t)\) volts with \(\omega =2000\) rad/sec. The amplitude of the current is closest to:
1. \(2\) A
2. \(3.3\) A
3. \(\frac{2}{\sqrt{5}}\)
4. \(\sqrt{5}~\text{A}\)
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. |  |
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