Mutual Induction

Q. An ideal transformer has $500$ primary turns and $10$ secondary turns. The primary coil carries current $2A$ and its voltage is $11,000V$. Current and voltage in the secondary coil will be

1. $100A,220V$
2. $0.04A,220V$
3. $100A,550000V$
4. $0.04A,550000V$

Q. Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

1. The currents in the two coils
2. The rates at which currents are changing in the two coils
3. Relative position and orientation of the two coils
4. The materials of the wires of the coils

Q. Two conducting circular loops of radii $R_{1}and{R}_2$ are placed in the same plane with their centres coinciding. If $R_1\gg R_2$, the mutual inductance M between them will be directly proportional to

1. $\frac{R_1}{R_2}$
2. $\frac{R_2}{R_1}$
3. $\frac{R_1^2}{R_2}$
4. $\frac{R_2^2}{R_1}$

Q. Figure shows two coaxial coils $M$ and $N$. Column I is regarding some operations done with coil $M$ and Column II about induced current in coil $N$.

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{i}& \text{Just after switch S is closed}& \text{a}& \text{Current is induced A to B}\\ \text{ii}& \text{Switch S is opened after}& \text{b}& \text{Current is induced from B to}\\ & \text{keeping it closed for a long}& & \text{A}\\ \text{iii}& \text{After switch S is closed for a}& \text{c}& \text{Nocurrent is induced}\\ & \text{long time}& & \end{array}$

1. i - a; ii - b; iii - c
2. i - a; ii - c; iii - b
3. i - c; ii - b; iii -a
4. i - b; ii - a; iii -c

Q. Two conducting circular loops of radii $R_{1}and{R}_2$ are placed in the same plane with their centres coinciding. If $R_1\gg R_2$, the mutual inductance M between them will be directly proportional to

1. $\frac{R_1}{R_2}$
2. $\frac{R_2}{R_1}$
3. $\frac{R_1^2}{R_2}$
4. $\frac{R_2^2}{R_1}$

Q. The figure shows a solenoid carrying time varying current $I=I_{0}t$. On the axis of this solenoid a ring has been placed. The mutual inductance of the ring and the solenoid is $M$ and the self inductance of the ring is $L$. If the resistance of the ring is $R$ then the maximum current which can flow through the ring is equal to

1. $\frac{(2M+L)I_0}{R}$
2. $\frac{M{I}_0}{R}$
3. $\frac{(2M-L)I_0}{R}$
4. $\frac{(M+L)I_0}{R}$

Q.

In a transformer, the coefficient of mutual inductance between the primary and the secondary coil is 0.2 henry. When the current changes by 5 ampere/second in the primary coil, the induced e.m.f. in the secondary coil will be

1. 5 V

2. 1 V

3. 25 V

4. 10 V

Q. The magnetic flux linked with a coil changes by $2\times {10}^{-3}$ wb, When current in the neighbouring coil changes by 0.01 A. The coefficient of mutual induction of the coils is

1. 2 H
2. 20 H
3. 0.2 H
4. 200 H

Q. Two coils (1) & (2) are placed as shown in figure. Coefficient of mutual induction between (1) & (2) is M = 6 H. Find induced emf & induced current in coil (2). (R of coil (2) is $4\Omega )$

1. emf = 24 V, i = 0
2. emf = 0, i = 6A
3. emf = 24 V, i = 6A
4. emf = 0, i = 0

Q. A rectangular loop of sides 8 cm and 2 cm with a small break in it is moving out of a region of uniform magnetic field of 0.3 T, directed normal to the loop. At a particular instant, half of the loop is outside the magnetic field and half is inside the magnetic field. What is the emf developed across the break if the velocity of the loop is 1 $cm{s}^{-1}$ in a direction normal to the longer side of the loop ?

1. 0.06 mV
2. 0.12 mV
3. 0.18 mV
4. 0.24 mV

Q. Coefficient of mutual induction between 2 coils is 0.4 H. If a current of 4A in the primary is cut off in $\frac{1}{15000}$ second, the emf induced in the secondary is

1. 24 KV
2. 15 KV
3. 30 KV
4. 10 KV

Q. The figure shows a solenoid carrying time varying current $I=I_{0}t$. On the axis of this solenoid a ring has been placed. The mutual inductance of the ring and the solenoid is $M$ and the self inductance of the ring is $L$. If the resistance of the ring is $R$ then the maximum current which can flow through the ring is equal to

1. $\frac{(2M+L)I_0}{R}$
2. $\frac{M{I}_0}{R}$
3. $\frac{(2M-L)I_0}{R}$
4. $\frac{(M+L)I_0}{R}$

Q. Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation $I=I_o$sin ωt, where $I_o$= 10A and ω = 100$\Pi$ radian/sec. The maximum value of e.m.f. in the second coil is

1. $2\Pi$
2. $5\Pi$
3. $\Pi$
4. $4\Pi$

Q. A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current starts flowing through the coil. If $I_1$ is the current induced in the ring, and $B$ is the magnetic field at the axis of the coil due to $I_2$, then as a function of time $(t>0),$ the product $I_2$ (t) B(t)

1. Increases with time
2. Decreases with time
3. Does not vary with time
4. Passes through a maximum

Q. Coefficient of mutual induction between 2 coils is 0.4 H. If a current of 4A in the primary is cut off in $\frac{1}{15000}$ second, the emf induced in the secondary is

1. 24 KV
2. 15 KV
3. 30 KV
4. 10 KV

Q.

A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current $I_1\left(t\right)$ starts flowing through the coil. If $I_2\left(t\right)$ is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to $I_1\left(t\right)$, then the product of $I_2\left(t\right)$ and B(t)

1. Increases with time

2. Decreases with time

3. Does not vary with time

4. Passes through a maximum

Q. In a car spark-coil, when the current in the primary is reduced from $4.0\text{A}$ to $\text{zero}$ in $10\mu \text{s}$, an emf of $40,000\text{V}$ is induced in the secondary coil. Find the mutual inductance $M$ of the primary and the secondary windings of the spark coil.

1. $0.2\text{H}$
2. $0.1\text{H}$
3. $0.3\text{H}$
4. None

Q. A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current starts flowing through the coil. If $I_1$ is the current induced in the ring, and $B$ is the magnetic field at the axis of the coil due to $I_2$, then as a function of time $(t>0),$ the product $I_2$ (t) B(t)

1. Increases with time
2. Decreases with time
3. Does not vary with time
4. Passes through a maximum

Q. Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation $I=I_{0}sin\omega t$, where $I_0=10Aand\omega =100\pi radian/sec$. The maximum value of e.m.f. in the second coil is

1. $2\pi$
2. $5\pi$
3. $\pi$
4. $4\pi$

Q. Two concentric circular coils $X$ and $Y$ of radii $16\text{cm}$ and $10\text{cm}$ respectively lie in same vertical plane containing the north-south direction. Coil $X$ has $20$ turns and carries a current of $16\text{A}$, coil $Y$ has $25$ turns and carries a current of $18\text{A}$. The sense of current in $X$ is anticlockwise and in coil $Y$ it is clockwise, for an observer looking at the coils, facing the west.
The magnitude and direction of the magnetic field at their common centre is:
(Neglect horizontal component of Earth's magnetic field)

1. $9\pi \times {10}^{-4}\text{T}$ towards the west
2. $9\pi \times {10}^{-4}\text{T}$ towards the east
3. $5\pi \times {10}^{-4}\text{T}$ towards the west
4. $4\pi \times {10}^{-4}\text{T}$ towards the east

Q. In a car spark-coil, when the current in the primary is reduced from $4.0\text{A}$ to $\text{zero}$ in $10\mu \text{s}$, an emf of $40,000\text{V}$ is induced in the secondary coil. Find the mutual inductance $M$ of the primary and the secondary windings of the spark coil.

1. $0.2\text{H}$
2. $0.1\text{H}$
3. $0.3\text{H}$
4. None

Q. What is the mutual inductance of a two-loop system as shown with centre separation l

1. $\frac{{\mu }_o\pi a^4}{8l^3}$
2. $\frac{{\mu }_o\pi a^4}{4l^3}$
3. $\frac{{\mu }_o\pi a^4}{6l^3}$
4. $\frac{{\mu }_o\pi a^4}{2l^3}$

Q.

A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current $I_1\left(t\right)$ starts flowing through the coil. If $I_2\left(t\right)$ is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to $I_1\left(t\right)$, then the product of $I_2\left(t\right)$ and B(t)

1. Increases with time

2. Decreases with time

3. Does not vary with time

4. Passes through a maximum

Q. Two coils have self-inductances $L_1=8mH$ and $L_2=4mH$. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the current, the induced voltage and the energy stored in the first coil are $i_1,V_1$ and $W_1$. Corresponding values for the second coil are $i_2,V_2$ and $W_2$ respectively. Then:
(IIT-JEE 1994)

1. $\frac{i_1}{i_2}=4$
2. $\frac{V_1}{V_2}=\frac{1}{4}$
3. $\frac{W_1}{W_2}=\frac{1}{2}$
4. $\frac{i_1}{i_2}=\frac{1}{4}$

Q.

The mutual inductance between two coils is 1.25 henry. If the current in the primary coil changes at a rate of 80 ampere/second, then the induced e.m.f. in the secondary coil is

1. 12.5 V

2. 64.0 V

3. 0.016 V

4. 100.0 V