Tag: mutual inductance

Questions Related to mutual inductance

Two coils P and Q are lying parallels and very close to each other. Coil P is connected to an AC source whereas Q is connected to a sensitive galvanometer. On pressing key K

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. small variations are observed in the galvanometer for applied 50 Hz voltage

  2. deflections in the galvanometer can be observed for applied voltage of 1 Hz to 2 Hz.

  3. no deflection in the galvanometer will be observed

  4. constant deflection will be observed in the galvanometer for 50 Hz supply voltage

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Correct Option: B
Explanation:

Upon connecting to the AC source , a current starts to flow in the coil P. This current induces a current in the galvanometer coil Q due to mutual  inductance because of the flux linkages. This induced current causes a deflection in the galvanometer.

The value of mutual inductance can be increased by

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. decreasing N

  2. increasing N

  3. winding the coil on wooden frame

  4. winding the coil on china clay

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Correct Option: B
Explanation:

$M = \mu N _1 N _2 \dfrac{ Area _{12}}{length _{12}} $


$ Area _{12} $ - area in common to both the coils where the flux links both of them together.
$length _{12}$ - length in common to both the coils where the flux links both of them together.
Therefore to increase the mutual inductance, the number of turns can be increased.  

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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

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

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

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

  4. 0

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Correct Option: D

A coil of wire has 0.2 m radius and 500 turns. It carries a current of 1 A.The magnetic induction at the centre of the coil is 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $1.5\times { 10 }^{ -3 }T$

  2. $1.6\times { 10 }^{ -3 }T$

  3. $1.7\times { 10 }^{ -3 }T$

  4. $1.8\times { 10 }^{ -3 }T$

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Correct Option: B

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.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $100 \mu H$

  2. $50 \mu H$

  3. $20 \mu H$

  4. $60 \mu H$

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Correct Option: A

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?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

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

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Correct Option: C

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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

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

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

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

  4. $0$

Show answer
Correct Option: D

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.