A circular coil of radius 5 cm has 500 turns of a wire. The approximate value of the coefficient of self induction of the coil will be -

1.  $25<mspace\; width="1em"></mspace>\mathrm{mH}$                           

2.  $25\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{mH}$

3.  $50\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{mH}$               

4.  $50\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{H}$

A coil of radius 1 cm and  turns 100 is placed in the middle of a long solenoid of radius 5 cm and having 8 turns/cm. The mutual induction in millihenry will be-

1.  0.0316                   

2.  0.063 

3.  0.105                     

4.  Zero

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.  $10<mspace\; width="1em"></mspace>\mathrm{\mu V}$                           

2.  $20<mspace\; width="1em"></mspace>\mathrm{\mu V}$

3.  $30<mspace\; width="1em"></mspace>\mathrm{\mu V}$                           

4.  $40<mspace\; width="1em"></mspace>\mathrm{\mu V}$

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 long solenoid having 1000 turns per cm is carrying alternating current of one ampere peak value. A search coil of area of cross-section $1\times {10}^{-4}<mspace\; width="1em"></mspace>{\mathrm{m}}^2$ 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 $2.5\times {10}^{-2}<mspace\; width="1em"></mspace>\mathrm{V}$. 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

A coil of the area $7<mspace\; width="1em"></mspace>{\mathrm{cm}}^2$ 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.  $0.64<mspace\; width="1em"></mspace>\mathrm{mA}$                     

2.  $1.05<mspace\; width="1em"></mspace>\mathrm{mA}$ 

3.  $1.75<mspace\; width="1em"></mspace>\mathrm{mA}$                     

4.  $2.60<mspace\; width="1em"></mspace>\mathrm{mA}$

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 $\mathrm{t}<mspace\; width="1em"></mspace>=\mathrm{\tau }<mspace\; width="1em"></mspace>{\log }_{\mathrm{e}}<mspace\; width="1em"></mspace>10$, 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 $\mathrm{i}={\mathrm{i}}_0{\mathrm{e}}^{-\mathrm{t}/\mathrm{\tau }}$

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 : $\mathrm{\epsilon }=\frac{-\mathrm{d\varphi }}{\mathrm{dt}}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\Rightarrow <mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\mathrm{\epsilon }=0<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\mathrm{when}<mspace\; width="1em"></mspace>\mathrm{\varphi }=0$

(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.

An emf of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t = $\infty$ and at t = 1 second is?

1.  $\frac{{\mathrm{e}}^{1/2}}{{\mathrm{e}}^{1/2}-1}$                               

2.  $\frac{{\mathrm{e}}^2}{{\mathrm{e}}^2-1}$

3.  $1-{\mathrm{e}}^{-1}$                           

4.  ${\mathrm{e}}^{-1}$