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
| 1. | \(1.59~\text{kHz}\) | 2. | \(15.9~\text{rad/s}\) |
| 3. | \(15.9~\text{kHz}\) | 4. | \(1.59~\text{rad/s}\) |
A series \(RC\) circuit is connected to an alternating voltage source. Consider two situations:
(1) When the capacitor is air-filled.
(2) When the capacitor is mica filled.
The current through the resistor is \(i\) and the voltage across the capacitor is \(V\) then:
1. \(V_a< V_b\)
2. \(V_a> V_b\)
3. \(i_a>i_b\)
4. \(V_a = V_b\)
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. \(0.33\)
In a box \(Z\) of unknown elements (\(L\) or \(R\) or any other combination), an ac voltage \(E = E_0 \sin(\omega t + \phi)\) is applied and the current in the circuit is found to be \(I = I_0 \sin\left(\omega t + \phi +\frac{\pi}{4}\right)\). The unknown elements in the box could be:
| 1. | Only the capacitor |
| 2. | Inductor and resistor both |
| 3. | Either capacitor, resistor, and an inductor or only capacitor and resistor |
| 4. | Only the resistor |
A direct current of \(5~ A\) is superimposed on an alternating current \(I=10sin ~\omega t\) flowing through a wire. The effective value of the resulting current will be:
| 1. | \(15/2~A\) | 2. | \(5 \sqrt{3}~A\) |
| 3. | \(5 \sqrt{5}~A\) | 4. | \(15~A\) |
1. \(0.707~\text A\)
2. \(1~\text A\)
3. \(1.414~\text A\)
4. \(2~\text A\)
| 1. | \(\omega L~I_0\sin\omega t\) | 2. | \(\frac{{I}_0}{\omega{L}}\sin\omega t\) |
| 3. | \(\frac{{I}_0}{\omega{L}}\cos\omega t\) | 4. | \(\omega L~I_0\cos\omega t\) |
| 1. | circuit will be capacitive if \(\omega>\frac{1}{\sqrt{LC}} \) |
| 2. | circuit will be inductive if \(\omega=\frac{1}{\sqrt{LC}} \) |
| 3. | power factor of circuit will be unity if capacitive reactance equals inductive reactance |
| 4. | current will be leading voltage if \(\omega>\frac{1}{\sqrt{LC}} \) |
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