Inductors in Circuits

Q. Figure shows a circuit contains three identical resistors with resistance $R=9.0\Omega$each, two identical inductors with inductance, L = 2.0 mH each, and an ideal battery with emf $\epsilon =18V$. The current ${}^{\prime }{i}^{\prime }$ through the battery just after the switch closed is

1. 0.2 A
2. 0 A
3. 2 A
4. 2 mA

Q. A potentiometer arrangement is shown in the figure. Driving cell has e.m.f. $e$ and internal resistance $r$. Resistance of potentiometer wire $\text{AB}$ is $R.\text{F}$ is the cell of e.m.f. $\frac{e}{3}$ and internal resistance $\frac{r}{3}$. Balance point $\left(J\right)$ can be obtained for all finite values of

1. $R>\frac{r}{2}$
2. $R<\frac{r}{2}$
3. $R>\frac{r}{3}$
4. $R<\frac{r}{3}$

Q. 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 decreasing at a rate of ${10}^3{As}^{-1}$ then potential difference between $A$ and $B$ ($V_B-V_A$ ) is equal to

1. $20V$
2. $15V$
3. $10V$
4. $5V$

Q.

How is potential difference calculated?

Q. 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 $t=\infty$ and at t =1 second is

1. $e^{-1}$
2. $\frac{e^{\frac{1}{2}}}{e^{\frac{1}{2}}-1}$
   
3. $\frac{e^2}{e^2-1}$
   
4. $1-e^{-1}$
   

Q. Dimensions of a block are $1cm\times 1cm\times 100cm$. If specific resistance of its material is $3\times {10}^{-7}$ ohm - m, then the resistance between it’s opposite rectangular faces is

1. $3\times {10}^{-9}$ ohm
2. $3\times {10}^{-7}$ ohm
3. $3\times {10}^{-5}$ ohm
4. $3\times {10}^{-3}$ ohm

Q. In the circuit shown in the figure, $C=6\mu \text{F}$. The charge stored in capacitor of capacity $C$ is-

1. Zero
2. $90\mu \text{C}$
3. $40\mu \text{C}$
4. $60\mu \text{C}$

Q. A long solenoid has 500 turns. When a current of 2 $A$ is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4\times {10}^{-3}$ $Wb$. The self-inductance of the solenoid is

1. $1.0H$
2. $2.5H$
3. $4.0H$
4. $2.0H$

Q.

The time taken for the magnetic energy to reach $25\%$ of its maximum value, when a solenoid of resistance $R$, inductance $L$ is connected to a battery, is

1. $\frac{L}{R}\ln \left(2\right)$

2. $\frac{L}{R}\ln \left(10\right)$

3. Infinite

4. $\frac{L}{R}\ln \left(5\right)$

Q.

The electric current in a discharging R-C circuit is given by $i=i_o{e}^{\frac{-t}{RC}}$ where $i_o$ , R and C are constant parameters and$\text{t}$ is time. Let $i_o$ = 2.00 A, R=$6\times {10}^5$ Ω and C = 0.500 $\mu$ F.

(a) Find the current at t = 0.3 s.

(b) Find the rate of change of current at t = 0.3 s

(c) Find approximately the current at t = 0.31 s.

Q. Consider the conducting square loop shown in the figure. In the given adjacent circuit , the switch is closed and after some time it is opened again, the closed loop will show-

1. A clockwise current-pulse
2. An anticlockwise current-pulse
3. An anticlockwise current-pulse and then a clockwise current-pulse
4. A clockwise current-pulse and then an anticlockwise current-pulse

Q. A parallel plate capacitor (without dielectric) is charged by a battery and kept connected to the battery. A dielectric slab of dielectric constant $‘k^{\prime }$ is inserted between the plates fully occupying the space between the plates. The energy density of electric field between the plates will:

1. Decrease $k$ times
2. Increase $k^2$ times
3. Decrease $k^2$ times
4. Increase $k$ times

Q.

Is inductance a function of frequency?

Q. An inductor of 2 henry and a resistance of 10 ohms are connected in series with a battery of 5 volts. The initial rate of change of current is

1. 0.25 amp/sec ​
2. 2.0 amp/sec
3. 0.5 amp/sec ​
4. 2.5 amp/sec

Q. An inductor $L$, a resistance $R$ and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance of coil having inductance $L$ is also $R$. Which of the following statement gives the correct description of the happenings, when the switch $S$ is closed ?

1. The bulb $B_2$ lights up earlier than $B_1$ and finally both the bulbs shine equally bright.
2. $B_1$ light up earlier and finally both the bulbs acquire equal brightness.
3. $B_2$ lights up earlier and finally $B_1$ shines brighter than $B_2$.
4. $B_1$ and $B_2$ light up together with equal brightness all the time.

Q. In an $L-R$ circuit connected to a battery of constant e.m.f $E$, switch S is closed at time t = 0. If e denotes the magnitude of induced e.m.f across inductor and i the current in the circuit at any time t. Then which of the following graphs shows the variation of $e$ with $i$ ?

1. 
2. 
3. 
4. 

Q. While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the x-y plane containing two small holes that act as two coherent point sources $(S_1,S_2)$ emitting light of wavelength 600 $nm$. The student mistakenly placed the screen parallel to the $x-z$ plane (for $z>0$) at a distance $D=3m$, from the mid-point of $S_1,S_2$, as shown schematically in the figure. The distance between the sources $d=0.6003mm$. The origin O is at the intersection of the screen and the line joining $S_1,S_2$. Which of the following is(are) true of the intensity pattern on the screen?

1. Semi circular bright and dark bands centered at point O
2. The region very close to the point O will be dark
3. Straight bright and dark bands parallel to the x-axis
4. Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction.

Q. Why is semiconductor damaged by strong current?

Q. In the circuit shown,


the switch $S_1$ is closed at time $t=0$ and the switch $S_2$ is kept open. At some time $\left(t_0\right)$ later, the switch $S_1$ is opened and $S_2$ is closed. The behaviour of the current $I$ as a function of time $t$ is given by:

1. 
2. 
3. 
4. 

Q. When the current in the portion of the circuit shown in the figure is $2\text{A}$ and increasing at the rate of $1\text{A/s}$, the measured potential difference $V_{ab}=8\text{V}$. However when the current is $2\text{A}$ and decreasing at the rate of $1\text{A/s}$, the measured potential difference $V_{ab}=4\text{V}$. The value of $R$ and $L$ are

1. $3\Omega$ and $2\text{H}$ respectively
2. $2\Omega$ and $3\text{H}$ respectively
3. $10\Omega$ and $6\text{H}$ respectively
4. $6\Omega$ and $1\text{H}$ respectively.

Q. Draw a circuit diagram of a C.E. transistor amplifier. Briefly explain its working and write the expression for (i) current gain, (ii) voltage gian of the amplifier.

Q. Figure shows three circuits with identical batteries, inductor and resistors. Rank the circuits in the decreasing order of the current through the battery just after the switch is closed

1. $i_2=i_3>i_1{i}_1\ne 0$
2. $i_2=i_3=i_1{i}_1=0$
3. $i_2<i_3<i_1{i}_1\ne 0$
4. $i_2>i_3>i_1{i}_1=0$

Q. Three capacitors each having capacitance $C=2\mu \text{F}$ are connected with a battery of e.m.f. $30\text{V}$ as shown in the figure. When the switch $S$ is closed, the extra amount of charge flown through the battery is

1. $20\mu \text{C}$
2. $10\mu \text{C}$
3. $24\mu \text{C}$
4. $40\mu \text{C}$

Q.

What is armature voltage?

Q. Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel with each other across an external resistance R. What is the current through this resistance ?

Q. A solenoid $1.0\text{m}$ long and $0.05\text{m}$ diameter has $700$ turns. Another solenoid of 50 turns is tightly wound over the first solenoid. Find the emf induced in the second solenoid when the current in the first solenoid changes from $0$ to $5\text{A}$ in $0.01\text{s}$.

1. $4.3\times {10}^{-2}\text{V}$
2. $2.1\times {10}^{-2}\text{V}$
3. $4.3\times {10}^{-3}\text{V}$
4. $2.1\times {10}^{-3}\text{V}$

Q. A coil of inductance 8.4 mH and resistance $6\Omega$ is connected to a 12 V battery. The current in the coil is 1.0 A at approximately the time

1. 20 sec ​
2. 35 milli sec ​
3. 1 milli sec ​
4. 500 sec ​

Q. A metal rod of length $10cm$ and a rectangular cross-section of $1cm\times \frac{1}{2}cm$ is connected to a battery across opposite faces. The resistance will be

1. maximum when the battery is connected across$1cm\times \frac{1}{2}cm$ faces
2. same irrespective of the three faces
3. maximum when the battery is connected across $10cm\times \frac{1}{2}cm$ faces.
   
4. maximum when the battery is connected across $10cm\times 1cm$ faces

Q.

The current in a discharging LR circuit is given by $i=i_{0}e-t\tau$ where \tau is the time constant of the circuit. Calculate the rms current for the period t = 0 to $t=\tau$.

Q. The emf of a battery is 2V and internal resistance is 0.5 ohm . Find the maximum power that can be delivered by the cell.