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

Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity. If the wire AB is replaced by semicircular wire, the magnitude of the induced current will 

(1) Increase

(2) Remain the same

(3) Decrease

(4) Increase or decrease depending on whether the semicircle bulges towards the resistance or away from it

The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be 

(1) $\frac{1}{4}L$

(2) L

(3) 4 L

(4) 16 L

A thin semi-circular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction $\overrightarrow{\mathrm{B}}$ (see figure).

At the position MNQ the speed of the ring is v and the potential difference developed across the ring is

1. zero 

2. ${\mathrm{Bv\pi R}}^2 /2$ and M is at higher potential 

3. $\mathrm{\pi RBv}$ and Q is at higher potential 

4. $2\mathrm{RBv}$ and Q is at higher potential.

The current i in an induction coil varies with time t according to the graph shown in figure. Which of the following graphs shows the induced emf (e) in the coil with time

(1)

(2)

(3)

(4)

A uniform but time-varying magnetic field $\mathrm{B}\left(\mathrm{t}\right)$ exists in a circular region of radius $\mathrm{a}$ and is directed into the plane of the paper, as shown.

The magnitude of the induced electric field at point $\mathrm{P}$ at a distance $\mathrm{r}$ from the centre of the circular region :

1.  is zero                             

2.  decreases as $1/\mathrm{r}$ 

3.  increases as $\mathrm{r}$               

4.  decreases as $1/{\mathrm{r}}^2$

A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of

(1) $\frac{mgR}{Bl}$

(2) $\frac{mgR}{B^2{l}^2}$

(3) $\frac{mgR}{B^3{l}^3}$

(4) $\frac{mgR}{B^{2}l}$

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

1. \(5~\text{V}\)
2. \(10~\text{V}\)
3. \(15~\text{V}\)
4. \(20~\text{V}\)

The magnetic flux through a coil varies with time as $\mathrm{\varphi }= 5{\mathrm{t}}^2+6\mathrm{t}+9$. The ratio of emf at t = 3s to t = 0s will be 

1.  1 : 9                           

2.  1 : 6 

3.  6 : 1                           

4.  9 : 1

In the figure magnetic energy stored in the coil is 

(1) Zero

(2) Infinite

(3) 25 joules

(4) None of the above