Q. No.| 1. | \(484~\text{W}\) | 2. | \(848~\text{W}\) |
| 3. | \(400~\text{W}\) | 4. | \(786~\text{W}\) |
| 1. | \(\frac{\varepsilon^{2} R}{\left[R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}\right]}\) | 2. | \(\frac{\varepsilon^{2} \sqrt{R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}}}{R}\) |
| 3. | \(\frac{\varepsilon^{2}\left[R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}\right]}{R}\) | 4. | \(\frac{\varepsilon^{2}R}{\sqrt{R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}}}\) |
| 1. | \(0.67~\text{W}\) | 2. | \(0.78~\text{W}\) |
| 3. | \(0.89~\text{W}\) | 4. | \(0.46~\text{W}\) |
| 1. | \(\dfrac{E_{0}^{2}}{R} \sin^{2}\omega t\) | 2. | \(\dfrac{E_{0}^{2}}{R}\cos^{2}\omega t\) |
| 3. | \(\dfrac{E_{0}^{2}}{R}\) | 4. | \(\text{zero}\) |
1. \(200~\text W\)
2. \(400~\text W\)
3. \(300~\text W\)
4. zero
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. | \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\) |
The potential differences across the resistance, capacitance and inductance are \(80\) V, \(40\) V and \(100\) V respectively in an \(LCR\) circuit.
What is the power factor of this circuit?
1. \(0.4\)
2. \(0.5\)
3. \(0.8\)
4. \(1.0\)
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. \(0.33\)
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. | \(\dfrac{E^2_0}{\sqrt{2}R}\) | 2. | \(\dfrac{E^2_0}{4R}\) |
| 3. | \(\dfrac{E^2_0}{2R}\) | 4. | \(\dfrac{E^2_0}{8R}\) |
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