Q. No.
1. \({{3}\over{\ln\left({1.2}\right)}}\)
2. \({{6}\over{\ln\left({1.2}\right)}}\)
3. \({{3}\over{\ln\left({1.8}\right)}}\)
4. \({{6}\over{\ln\left({2.4}\right)}}\)
1. \(18~\text{V}\)
2. \(-18~\text{V}\)
3. \(9~\text{V}\)
4. \(-9~\text{V}\)
A coil of inductance \(2\text{ H}\) having negligible resistance is connected to a source of supply whose voltage is given by \(V = 3t \) volt. (where \(t\) is in second). If the voltage is applied when \(t = 0\), then the energy stored in the coil after \(4\text{ s}\) is:
1. \(73 \mathrm{~J}\)
2. \(36 \mathrm{~J}\)
3. \(144 \mathrm{~J}\)
4. \(288 \mathrm{~J}\)
The current (\(i\)) at time \(t=0\) and \(t=\infty\) respectively for the given circuit is:
1. \( \frac{18 \mathrm{E}}{55}, \frac{5 \mathrm{E}}{18} \)
2. \( \frac{10 \mathrm{E}}{33}, \frac{5 \mathrm{E}}{18} \)
3. \( \frac{5 \mathrm{E}}{18}, \frac{18 \mathrm{E}}{55} \)
4. \(\frac{5 \mathrm{E}}{18}, \frac{10 \mathrm{E}}{33}\)
Figure shows a circuit that contains four identical resistors with resistance \(R=2.0~\Omega\), two identical inductors with inductance \(L=2.0~\mathrm{mH}\) and an ideal battery with emf \(E=9~V\). The current '\(i\)' just after the switch '\(s\)' is closed will be:
1. \(2.25~\mathrm{A}\)
2. \(3.0~\mathrm{A}\)
3. \(3.37~\mathrm{A}\)
4. \(9~\mathrm{A}\)
(take \({e}^2=7.389\) )
1. \(1.06\)
2. \(0.84\)
3. \(1.46\)
4. \(1.15\)
A series \(L\text-R\) circuit is connected to a battery of emf \(V\). If the circuit is switched on at \(t=0\), then the time at which the energy stored in the inductor reaches (\(\frac{1}{n}\)) times of its maximum value, is :
1. \( \frac{L}{R} \ln \left(\frac{\sqrt{n}-1}{\sqrt{n}}\right) \)
2. \( \frac{L}{R} \ln \left(\frac{\sqrt{n}}{\sqrt{n}-1}\right) \)
3. \( \frac{L}{R} \ln \left(\frac{\sqrt{n}}{\sqrt{n}+1}\right) \)
4. \(\frac{L}{R} \ln \left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)\)
An electrical circuit segment contains a \(50~\text{mH}\) inductor in series with a \(30~\text{V}\) source and a \(2~\Omega\) resistor, connected between points \(P\) and \(Q\) as shown. At a certain instant, the current through the circuit is \(1~\text{A}\) and is decreasing at a rate of \(100~\text{A/s}.\) What is the potential difference \((V_P-V_Q)\) at that instant?
| 1. | \(10\) V | 2. | \(25\) V |
| 3. | \(33\) V | 4. | \(53\) V |
1. \(5.5~\text{A}\)
2. \(7.5~\text{A}\)
3. \(3~\text{A}\)
4. \(6~\text{A}\)
Consider the \(LR\) circuit shown in the figure. If the switch \(S\) is closed at \(t=0\) then the amount of charge that passes through the battery between \(t=0\) and \(t=\frac{L}{R}\) is:
1. \(\frac{7.3EL}{R^2}\)
2. \(\frac{2.7EL}{R^2}\)
3. \(\frac{EL}{7.3R^2}\)
4. \(\frac{EL}{2.7R^2}\)
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