The key \(K\) is inserted at time \(t=0\). The initial \((t=0)\) and final \(t\rightarrow \infty\) currents through the battery are:
                              

1. \(\frac{1}{15}~\text{A},~\frac{1}{10}~\text{A}\)
2. \(\frac{1}{10}~\text{A},~\frac{1}{15}~\text{A}\)
3. \(\frac{2}{15}~\text{A},~\frac{1}{10}~\text{A}\)
4. \(\frac{1}{15}~\text{A},~\frac{2}{25}~\text{A}\)

A solenoid has an inductance of 60 henry and a resistance of 30 ohms. If connected to a 100-volt battery, how long will it take for the current to reach $\frac{e - 1}{e} \approx 63.2\%$ of its final value?

1.  1 second

2.  2 seconds

3.  e seconds

4.  2e seconds

The network shown in the figure is part of a complete circuit. If at a certain instant, the current \(I\) is \(5~\text{A}\) and it is decreasing at a rate of $\mathrm{}$\(5\times 10^{3}~\text{A/s}\), then ${\mathrm{}}_{}$\(V_B-V_A\) is equal to: 

The adjoining figure shows two bulbs \(B_1\) and \(B_2\) resistor \(R\) and an inductor \(L\). When the switch \(S\) is turned off 

An inductance L and a resistance R are first connected to a battery. After some time the battery is disconnected but L and R remain connected in a closed circuit. Then the current reduces to 37% of its initial value in time ?

1. RL sec

2. $\frac{R}{L}sec$

3. $\frac{L}{R}sec$

4. $\frac{1}{LR}sec$

An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t = ∞ and at t = 1 second is 

1. $\frac{e^{1/2}}{e^{1/2}-1}$

2. $\frac{e^2}{e^2-1}$

3. 1 – e^–1

4. e^–1

Two conducting circular loops of radii \(R_1\) and \(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\), the mutual inductance \(M\) between them will be directly proportional to:

A circular loop of radius R carrying current I lies in the x-y plane with its centre at the origin. The total magnetic flux through the x-y plane is 

1. Directly proportional to I

2. Directly proportional to R

3. Directly proportional to R²

4. Zero

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be 

1. Maximum in situation (A)

2. Maximum in situation (B)

3. Maximum in situation (C)

4. The same in all situations

A conductor ABOCD moves along its bisector with a velocity of 1 m/s through a perpendicular magnetic field of 1 wb/m², as shown in fig. If all the four sides are of 1m length each, then the induced emf between points A and D is

1. 0

2. 1.41 volt

3. 0.71 volt

4. None of the above