Tag: electromagnetic induction

Questions Related to electromagnetic induction

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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

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

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

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

  4. $6 \times 10 ^ { - 5 }$ henry

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Correct Option: B

The inductance of a solenoid $0.5\ m$ long of cross-sectional area $20\ cm^2$ and with $500$ turns is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $12.5\ mH$

  2. $1.25\ mH$

  3. $15.0\ mH$

  4. $0.12\ mH$

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Correct Option: A

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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  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

Show answer
Correct Option: C
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. 

Which of the following units denotes the dimension $\dfrac {ML^2}{Q^2}$ where Q denotes the electric charge?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $Wb/m^2$

  2. $henry (H)$

  3. $H/m^2$

  4. $weber (Wb)$

Show answer
Correct Option: B
Explanation:
Mutual inductance $=\dfrac {\phi}{I}=\dfrac {BA}{I}$

$[Henry]=\dfrac {[MT^{-1}Q^{-1}L^2]}{[QT^{-1}]}=ML^2Q^{-2}$

The mutual inductance between two coils when a current of $5$ A changes to $10$ A in $1$ s and induces an emf of $100$ m V in the secondary is ______

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $20$ m H

  2. $10$ mH

  3. $30$ mH

  4. $15$ mH

Show answer
Correct Option: A
Explanation:

Mutual inductance$=M=\dfrac{emf}{\Delta I/t}$


$=\dfrac{100mV}{10-5}$

$=20mH$

Answer-(A)

Identify which of the following best describe the Mutual inductance?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  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.

Show answer
Correct Option: A
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.

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 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $20mH$

  2. $10mH$

  3. $1mH$

  4. $2mH$

Show answer
Correct Option: B
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$
$\displaystyle \therefore L=10\times 10^{-3}=10mH$

Two coils have a mutual inductance of $0.005\ H$. The current changes in the first coil according to equation $I=I _0sin\omega t$, where $I _0=10A$ and $\omega=100\pi rad/s$. The maximum value of emf (in volt) in the second coil is.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $2\pi$

  2. $5\pi$

  3. $\pi$

  4. $4\pi$

Show answer
Correct Option: B
Explanation:

$EMF=\frac {MdI}{dt}$
$=(0\cdot 005)I _0 w cos wt$
Maximum EMF$=(0\cdot 005)\times 10\times 100\pi$
$=5\pi$

The mutual inductance of the system of two coils is $5mH$. The current in the first coil varies according to the equation $I={ I } { o }\sin { wt } $ where ${ I } _{ o }=10A$ and $W=100\pi \, rad/s$. The value of maximum induced emf in the second coil is ______

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $2\pi V$

  2. $\pi V$

  3. $5\pi V$

  4. $4\pi V$

Show answer
Correct Option: C
Explanation:

$Emf=M\cdot \cfrac { di }{ dt } =5\times { 10 }^{ -3 }\times { I } _{ o }\omega \cos { \omega t } \ { \left( Emf \right)  } _{ max }=5\times { 10 }^{ -3 }\times { I } _{ o }\omega =5\times { 10 }^{ -3 }\times 10\times 100\pi =5\pi V$

A short solenoid of length $4cm$, radius $2cm$ and $100$ turns is placed inside and on the axis of a long solenoid of length $80cm$ and $1500$ turns. A current of $3A$ flows through the short solenoid. The mutual inductance of two solenoids is

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $0.012H$

  2. $5.3\times {10}^{-5}H$

  3. $5.91\times {10}^{-3}H$

  4. $8.3\times {10}^{-5}H$

Show answer
Correct Option: C
Explanation:

As $M = \cfrac{\mu _0N _1N _2A}{l}$


where,
$A =$ common cross-sectional area
$l =$ length of small coil
$N _1 =$ No. of turns of small coil
$N _1 =$ No. of turns of long coil

$M = \cfrac{4\pi \times 10^{-7} \times 100 \times 1500 \times \pi \times (\cfrac{2}{100})^2}{(\cfrac{4}{100})} = 59157.6 \times 10^{-7} = 5.91 \times 10^{-3} H$