Q. No.\(1 .\) \(P \left(\frac{R}{Z}\right)^{2}\)
\(2 .\) \(P \sqrt{\frac{R}{Z}}\)
\(3 .\) \(P \left(\frac{R}{Z}\right)\)
\(4 .\) \(P\)
In an AC circuit, the current is given by; \(i=5\sin\left(100t-\frac{\pi}{2}\right)\) and the AC potential is \(V =200\sin(100 t)~\text V.\) The power consumption is:
1. \(20~\text W\)
2. \(40~\text W\)
3. \(1000~\text W\)
4. zero
A coil of inductive reactance of \(31~\Omega\) has a resistance of \(8~\Omega\). It is placed in series with a condenser of capacitive reactance \(25~\Omega\). The combination is connected to an AC source of \(110\) V. The power factor of the circuit is:
1. \(0.56\)
2. \(0.64\)
3. \(0.80\)
4. \(0.33\)
A resistance \(R\) draws power \(P\) when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes \(Z\), the power drawn will be:
| 1. | \(P\Big({\large\frac{R}{Z}}\Big)^2\) | 2. | \(P\sqrt{\large\frac{R}{Z}}\) |
| 3. | \(P\Big({\large\frac{R}{Z}}\Big)\) | 4. | \(P\) |
An inductor of \(20~\text{mH}\), a capacitor of \(100~\mu \text{F}\), and a resistor of \(50~\Omega\) are connected in series across a source of emf, \(V=10 \sin (314 t)\). What is the power loss in this circuit?
1. \( 0.79 ~\text{W} \)
2. \( 0.43 ~\text{W} \)
3. \( 2.74 ~\text{W} \)
4. \( 1.13 ~\text{W}\)
| 1. | resistive circuit | 2. | \({LC}\) circuit |
| 3. | inductive circuit | 4. | capacitive circuit |
The potential differences across the resistance, capacitance, and inductance are \(80~\text{V}\), \(40~\text{V}\) and \(100~\text{V}\) respectively in an \(LCR\) circuit. The power factor of this circuit is:
1. \(0.4\)
2. \(0.5\)
3. \(0.8\)
4. \(1.0\)
An AC source given by \(V=V_m\sin(\omega t)\) is connected to a pure inductor \(L\) in a circuit and \(I_m\) is the peak value of the AC current. The instantaneous power supplied to the inductor is:
| 1. | \(\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\) | 2. | \(-\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\) |
| 3. | \({V_mI_m}\mathrm{sin}^{2}(\omega t)\) | 4. | \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\) |
An AC voltage source is connected to a series \(LCR\) circuit. When \(L\) is removed from the circuit, the phase difference between current and voltage is \(\dfrac{\pi}{3}\). If \(C\) is instead removed from the circuit, the phase difference is again \(\dfrac{\pi}{3}\) between current and voltage. The power factor of the circuit is:
1. \(0.5\)
2. \(1.0\)
3. \(-1.0\)
4. zero
1. Pure resistive circuit
2. Pure capacitive circuit
3. Pure inductive circuit
4. None of the above
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