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A coil has an inductance of 2.5 H and a resistance of 0.5 r. If the coil is suddenly connected across a 6.0 volt battery, then the time required for the current to rise 0.63 of its final value is 
(1) 3.5 sec
(2) 4.0 sec
(3) 4.5 sec
(4) 5.0 sec

Pure inductance of 3.0 H is connected as shown below. The equivalent inductance of the circuit is

(1) 1 H
(2) 2 H
(3) 3 H
(4) 9 H

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) $\frac{1}{LR}sec$

In an LR-circuit, the time constant is that time in which current grows from zero to the value (where I₀ is the steady-state current) 
(1) 0.63 I₀
(2) 0.50 I₀
(3) 0.37 I₀
(4) I₀

In the figure magnetic energy stored in the coil is 

(1) Zero
(2) Infinite
(3) 25 joules
(4) None of the above

The core of a transformer is laminated to reduce energy losses due to  
(1) Eddy currents
(2) Hysteresis
(3) Resistance in winding
(4) None of these

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ >> R₂, the mutual inductance M between them will be directly proportional to 
(1) R₁/R₂
(2) R₂/R₁
(3) $R_1^2/R_2$
(4) $R_2^2/R_1$

A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to 
(1) l / L
(2) l² / L
(3) L/l
(4) L²/l

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 conducting rod PQ of length L = 1.0 m is moving with a uniform speed v = 2 m/s in a uniform magnetic field B = 4.0 T directed into the paper. A capacitor of capacity C = 10 μF is connected as shown in figure. Then

(1) q_A = + 80 μC and q_B = – 80 μC
(2) q_A = – 80 μC and q_B = + 80 μC
(3) q_A = 0 = q_B
(4) Charge stored in the capacitor increases exponentially with time

The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current, in descending order, through the battery (i) just after the switch is closed and (ii) a long time later:

The network shown in the figure is a part of a complete circuit. If at a certain instant the current i is 5 A and is decreasing at the rate of 10³ A/s then V_B – V_A is

(1) 5 V
(2) 10 V
(3) 15 V
(4) 20 V

Switch S of the circuit shown in the figure is closed at t = 0. If e denotes the induced emf in L and i denotes the current flowing through the circuit at time t, then which of the following graphs is correct?

1.		2.
3.		4.

A conducting square frame of side 'a' and a long straight wire carrying current i are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity v. The emf induced in the frame will be proportional to

1.1/x²
2.1/(2x-a)²
3.1/(2x+a)²
4. 1/(2x-a) x (2x+a)

A transformer having efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6A, the voltage across the secondary coil and the current in the primary coil respectively are
1. 300V,15A
2. 450V,15A
3. 450V,13.5A
4. 600V,15A

A uniform magnetic field of induction $\mathrm{B}$ is confined to a cylindrical region of radius $\mathrm{R}$. The magnetic field is increasing at a constant rate of $\frac{\mathrm{dB}}{\mathrm{dt}}$ (tesla/second). An electron of charge $\mathrm{q}$, placed at the point $\mathrm{P}$ on the periphery of the field experiences an acceleration of:
   

In the figure shown a square loop $\mathrm{PQRS}$ of side $‘\mathrm{a}’$ and resistance $‘\mathrm{r}’$ is placed near an infinitely long wire carrying a constant current $\mathrm{I}$. The sides $\mathrm{PQ}$ and $\mathrm{RS}$ are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by $180°$ about an axis parallel to the long wire and passing through the midpoints of the side $\mathrm{QR}$ and $\mathrm{PS}$. The total amount of charge which passes through any point of the loop during rotation is –
                       
1. $\frac{{\mathrm{\mu }}_0\mathrm{Ia}}{2\mathrm{\pi r}} \ln 2$
2. $\frac{{\mathrm{\mu }}_0\mathrm{Ia}}{\mathrm{\pi r}} \ln 2$
3. $\frac{{\mathrm{\mu }}_0{\mathrm{Ia}}^2}{2\mathrm{\pi r}}$
4. cannot be found because the time of rotation not given.

The current in an L – R circuit builds up to ${\left(3/4\right)}^{\mathrm{th}}$ of its steady state value in 4 seconds. The time constant of this circuit is?
1. $\frac{1}{\ln 2}\sec$                       
2. $\frac{2}{\ln 2}\sec$
3. $\frac{3}{\ln 2}\sec$                       
4. $\frac{4}{\ln 2}\sec$

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.  ${\mathrm{e}}^{-1}$

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. 

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.