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Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

The current in a coil is changed from 5 A to 10 A in $10^{-2}s$. Then, an emf of 50 m V is induced in a coil near by it. Calculate mutual inductance of two coils.

  1. $100 \mu H$

  2. $50 \mu H$

  3. $20 \mu H$

  4. $60 \mu H$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using E = M * (di/dt), we have 50 * 10^-3 = M * (5 / 10^-2). M = 50 * 10^-3 * 10^-2 / 5 = 10 * 10^-5 = 100 * 10^-6 H = 100 uH.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A short solenoid of radius  $a,$  number of turns per unit length  $n _ { 1 } ,$  and length  $L$  is kept coaxially inside a very long solenoid of radius  $b ,$  number of turns per unit length  $n _ { 2 } .$  What is the mutual inductance of the system?

  1. $\mu _ { 0 } \pi b ^ { 2 } n _ { 1 } n _ { 2 } L$

  2. $\mu _ { 0 } \pi a ^ { 2 } n _ { 1 } n _ { 2 } L ^ { 2 }$

  3. $\mu _ { 0 } \pi a ^ { 2 } n _ { 1 } n _ { 2 } L$

  4. $\mu _ { 0 } \pi b ^ { 2 } n _ { 1 } n _ { 2 } L ^ { 2 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mutual inductance of two coaxial solenoids is M = mu0 * pi * a^2 * n1 * n2 * L, where 'a' is the radius of the inner solenoid.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

  1. $\cfrac{{\mu} _{0}R}{2}$

  2. $\cfrac{{\mu} _{0}\pi R}{2}$

  3. $\cfrac{{\mu} _{0}}{2}$

  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a duplicate of 530253. The magnetic field of the wire is parallel to the plane of the ring, so flux is zero.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Two coils  $A$  and  $B$  having turns  $300$  and  $600$  respectively are placed near each other, on passing a current of  $3.0$  ampere in  $A$  the flux linked with  $A$  is  $1.2 \times 10 ^ { - 4 } weber$  and with  $B$  it is  $9.0 \times 10 ^ { - 5 } weber.$  The mutual  inductance of the system is

  1. $2 \times 10 ^ { - 5 }$ henry

  2. $3 \times 10 ^ { - 5 }$ henry

  3. $4 \times 10 ^ { - 5 }$ henry

  4. $6 \times 10 ^ { - 5 }$ henry
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mutual inductance M = Phi_B / I_A. Given Phi_B = 9.0 * 10^-5 Wb and I_A = 3.0 A, M = (9.0 * 10^-5) / 3.0 = 3.0 * 10^-5 H.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Two coils are placed close to each other. The mutual inductance of the pair of coils depend 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 coil
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mutual inductance between two coils is defined as the property of the coil due to which it opposes the change of current in the other coil. When the current in the neighboring coil changes, the flux sets up in the coil and because of this, changing flux emf is induced in the coil called Mutually Induced emf. 

So, it depends on the relative position and orientation of two coils. 

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Identify which of the following best describe the Mutual inductance?

  1. the ability of a current carrying conductor to induce a voltage in another conductor through a mutual magnetic field.

  2. the ability of current carrying conductor to produce a changing magnetic field.

  3. the ability of a conductor to induce a magnetic field in another current carrying conductor.

  4. the ability of a current carrying conductor to induce a current in another conductor through a mutual magnetic field.

  5. the ability of a magnetic field to induce a voltage in a current carrying conductor.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

As per the Faraday's experiments, a current in a conductor produces a magnetic field. This magnetic field gets linked with another conductor and result in an induced emf.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

For a current carrying inductor, emf associated in $20mV$. Now, current through it changes from $6A$ to $2A$ in $2s$. The coefficient of mutual inductance is 

  1. $20mH$

  2. $10mH$

  3. $1mH$

  4. $2mH$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle \left | e \right |=L\frac{dI}{dt}$
Here, $\displaystyle e=20mV=20\times 10^{-3}V$
Coefficient of mutual inductance,
$ 20\times 10^{-3}=L\times 2$
$\displaystyle \therefore L=10\times 10^{-3}=10mH$