In the circuit shown here, the point \(C\) is kept connected to point a till the current flowing through the circuit becomes constant. Afterward, suddenly, point \(C\) is disconnected from point \(A\) and connected to point \(B\) at time \(t=0\). The ratio of the voltage across resistance and the inductor at \(t=\frac{L}{R}\) will be equal to:
                        
1. \(1\)
2. \(-1\)
3. \(\dfrac{1-e}{e}\)
4. \(\dfrac{e}{1-e}\)

A \(20\) Henry inductor and coil is connected to a \(10~\Omega\) resistance in series as shown in the figure. The time at which the rated of dissipation of energy (Joule’s heat) across the resistance is equal to the rate at which magnetic energy is stored in the inductor, is:

 
1. \( \frac{1}{2} \ln 2 \)
2. \( \ln 2 \)
3. \( 2 \ln 2 \)
4. \( \frac{2}{\ln 2}\)

A coil of self inductance \(10~\text{mH}\) and resistance \(0.1~ \Omega\) is connected through a switch to a battery of internal resistance \(0.9~ \Omega\). After the switch is closed, the time taken for the current to attain \(80\%\) of the saturation value is: [take \(\ln 5=1.6\)]
1. \(0.324~\text{s}\)
2. \(0.002~\text{s}\)
3. \(0.103~\text{s}\)
4. \(0.016~\text{s}\)

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. \(\frac{EL}{2.7R^2}\)

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. \(\frac{L}{R} \ln \left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)\)

A part of a complete circuit is shown in the figure. At a certain instant, the current \(I\) is \(1~\text{A}\) and is decreasing at a rate of \(10^2~\text{A s}^{-1}.\)  The value of the potential difference \(V_P-V_Q\), (in volts) at that instant is:

         
1. \(10\)
2. \(25\)
3. \(33\)
4. \(53\)

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. \(9~\mathrm{A}\)

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. \(\frac{5 \mathrm{E}}{18}, \frac{10 \mathrm{E}}{33}\)

A coil of inductance \(2\) 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 \(4\) s is:
1. \(73 \mathrm{~J}\)
2. \(36 \mathrm{~J}\)
3. \(144 \mathrm{~J}\)
4. \(288 \mathrm{~J}\)