Assertion: When a coil is joined to a cell, the current through the cell will be 10% less than its steady-state value at time $\mathrm{t} =\mathrm{\tau } {\log }_{\mathrm{e}} 10$, where $\mathrm{\tau }$ is the time constant of the circuit.

Reason: When a coil is joined to a cell, the growth of current is given by $\mathrm{i}={\mathrm{i}}_0{\mathrm{e}}^{-\mathrm{t}/\mathrm{\tau }}$

1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false

Assertion: The magnetic flux linked with a coil is $\mathrm{\varphi }$, and the emf induced in it is $\mathrm{\epsilon }$. If $\mathrm{\varphi }=0$, $\mathrm{\epsilon }$ must be zero.

Reason : $\mathrm{\epsilon }=\frac{-\mathrm{d\varphi }}{\mathrm{dt}} \Rightarrow \mathrm{\epsilon }=0 \mathrm{when} \mathrm{\varphi }=0$

(a) Assertion and Reason both are correct and the Reason is the correct explanation of the Assertion.

(b) Assertion and Reason both are correct but the Reason is not the correct explanation of the Assertion.

(c) The assertion is correct but the Reason is wrong.

(d) Assertion and Reason both are wrong.

Assertion : The coil in the resistance boxes are made by doubling the wire.

Reason : Thick wire is required in resistance box.

A coil of the area $7 {\mathrm{cm}}^2$ and of 50 turns is kept with its plane normal to a magnetic field B. A resistance of 30 ohms is connected to the resistance-less coil. B is $75{\mathrm{e}}^{-200\mathrm{t}}$ Gauss. The current passing through the resistance at t = 5 ms will be-

1.  $0.64 \mathrm{mA}$                     

2.  $1.05 \mathrm{mA}$ 

3.  $1.75 \mathrm{mA}$                     

4.  $2.60 \mathrm{mA}$

A long solenoid having 1000 turns per cm is carrying alternating current of one ampere peak value. A search coil of area of cross-section $1\times {10}^{-4} {\mathrm{m}}^2$ and of 20 turns is placed in the middle of the solenoid so that its plane is perpendicular to the axis of the solenoid. The search coil registers a peak voltage $2.5\times {10}^{-2} \mathrm{V}$. The frequency of the current in the solenoid is -

1.  1.6 per second                   

2.  0.16 per second

3.  15.9 per second                 

4.  15.85 per second

Rate of increment of energy in an inductor with time in series LR circuit getting charge with battery of emf E is best represented by – [inductor has initially zero current]

1.                        

2. 

3.                        

4. 

A copper rod of length 0.19 m is moving parallel to a long wire with a uniform velocity of 10 m/s. The long wire carries 5 ampere current and is perpendicular to the rod. The ends of the rod are at distances 0.01 m and 0.2 m from the wire. The emf induced in the rod will be-

1.  $10 \mathrm{\mu V}$                           

2.  $20 \mathrm{\mu V}$

3.  $30 \mathrm{\mu V}$                           

4.  $40 \mathrm{\mu V}$

The magnetic flux through each turn of a 100 turn coil is $\left({\mathrm{t}}^3 – 2\mathrm{t}\right) \times {10}^{-3} \mathrm{Wb}$, where t is in second. The induced emf at t = 2 s is

1. $-4 \mathrm{V}$                       

2. $-1 \mathrm{V}$

3. $+1 \mathrm{V}$                       

4. $+4 \mathrm{V}$

Loop A of radius (r << R) moves towards loop B with a constant velocity v in such a way that their planes are always parallel.

What is the distance (x) between the two loops when the induced emf in loop A is maximum –

1. $\mathrm{R}$                                     

2. $\frac{\mathrm{R}}{\sqrt{2}}$

3. $\frac{\mathrm{R}}{2}$                                     

4. $\mathrm{R}\left(1-\frac{1}{\sqrt{2}}\right)$

The inductance of a closed-packed coil of 400 turns is 8 mH. A current of 5 mA is passed through it. The magnetic flux through each turn of the coil is approximately-

1.  $0.1 {\mathrm{\mu }}_0 \mathrm{Wb}$                     

2.  $0.2 {\mathrm{\mu }}_0 \mathrm{Wb}$

3.  $1.0 {\mathrm{\mu }}_0 \mathrm{Wb}$                     

4.  $2.0 {\mathrm{\mu }}_0 \mathrm{Wb}$