Tag: mutual inductance

Questions Related to mutual inductance

The coefficient of mutual inductance between two coils depends on

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. medium between the coils

  2. separation between the two coils

  3. orientation of the two coils

  4. all of the above

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Correct Option: D
Explanation:

The flux linked with two coils will depend upon the angle between the two coils. If their planes are parallel, then magnetic flux from one would completely  pass through the other. If the planes are perpendicular, no flux due to any of the coils would flow through the other.

The size of the two coils may be different which will affect the number of lines crossing the coil. The medium, if magnetic, will concentrate the field lines. Thus, all parameters would affect the inductance between them.

Two coils of self inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 10 mH

  2. 6 mH

  3. 4 mH

  4. 16 mH

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Correct Option: C
Explanation:

Given,

$L _1=2mH$
$L _2=8mH$
The mutual inductance between coil is 
$M=\sqrt{L _1L _2}$
$M=\sqrt{2\times 8}=\sqrt{16}mH$
$M=4mH$
The correct option is C.

A circular copper disc 10 cm in diameter rotates at 1800 revolution per minute about an axis through its centre and at right angles to disc. A uniform field of induction B of 1 Wb $m^2$ is perpendicular to disc. What potential difference is developed between the axis of the disc and the rim ?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 0.023 V

  2. 0.23 V

  3. 23 V

  4. 230 V

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Correct Option: B
Explanation:

Here, 

$l = r = 5\, cm = 5 \times 10^{-2} m,$
B = 1 Wb $m^{-2}$

$ \omega = 2 \pi \left( \dfrac{1800}{60} \right) \, rad \, s^{-1} = 60 \pi \, rad \, s^{-1},$

$\epsilon \, = \, \dfrac{1}{2} Bl^2 \omega \, =\, \dfrac{1}{2} \times 1 \times (5 \times 10^{-2})^2 \times 60 \pi = 0.23 V$

Mutual inductance of two coils can be increased by 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. decreasing the number of turns in the coils

  2. increasing the number of turns in the coils

  3. winding the coils on wooden cores

  4. none of these.

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Correct Option: B
Explanation:

As M  = $\dfrac{\mu _0N _1N _2A}{l} $ 
i.e M can be increased by increasing the numbers of turns in the coils.

If the self inductance of 500 turns coil is 125 mH, then the self inductance of the similar coil of 800 mH

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 48.8 mH

  2. 200 mH

  3. 290 mH

  4. 320 mH

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Correct Option: D
Explanation:

$L=\mu _o \mu _r N^2Al$
For similar coil, $A, l$ will be same 
So,   $ \, \dfrac{L _1}{L _2} = \dfrac{N _1^2}{N _2^2}$

$ L _{800}= \dfrac{N _{800} ^2}{N _{500}^2}\times L _{500}= \, \dfrac{125}{(500)^2} \, \times \, (800)^2 \, = \, 320 \, mH$

The mutual inductance $M _{12}$ of a coil 1 with respect to coil 2

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. increases when they are brought nearer

  2. depends on the current passing through the coils.

  3. increases when one of them is rotated about an axis.

  4. both (a) and (b) are correct

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Correct Option: A
Explanation:

Mutual Induction: Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighbouring coil or circuit will also change. Hence an emf will be induced in the neighbouring coil or circuit. This phenomenon is called ‘mutual induction’.


If the two coils $1$ and $2$ are present with mutual inductance $M _1$ and $M _2$. Then the mutual inductance of the coil 1 due to 2 increases when they are bought near since, mutual inductance is  proportional to the flux passed through the coil.

The mutual induction of $M _{12}$ is same as $M _{21}$

Match the following:

Quantity Formula
1) Magnetic flux linked with a coil a) $\displaystyle -N\frac { d\phi  }{ dt } $
2) Induced emf b) $\displaystyle { \mu  } _{ r }{ \mu  } _{ 0 }{ n } _{ 1 }{ n } _{ 2 }{ \pi r } _{ 1 }^{ 2 }l$
3) Force on a charged particle moving in a electric and magnetic field c) $\displaystyle BA\cos { \theta  } $
4) Mutual inductance of a solenoid d) $\displaystyle q\left( \overline { E } +\overline { v } \times \overline { B }  \right) $
mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 1-c, 2-d, 3-b, 4-a

  2. 1-c, 2-a, 3-d, 4-b

  3. 1-b, 2-a, 3-c, 4-d

  4. 1-a, 2-b, 3-d, 4-c

Show answer
Correct Option: B
Explanation:

1) Magnetic flux through any area is the scalar product of its area vector with the magnetic field vector. Thus for a coil, it is $\vec{B}.\vec{A}=BAcos\theta$

2) Emf induced in a coil due to changing flux through it is given by Faraday's Law,
$Emf = -N\dfrac{d\phi}{dt}$
3) Force on a charged particle due to electric field = $q\vec{E}$
Force on a moving charged particle due to magnetic field = $q(\vec{v}\times \vec{B})$
Thus, force on a moving charged particle in an electric and magnetic field = $q(\vec{E}+\vec{v}\times \vec{B})$
4) Mutual inductance of a solenoid is found out to be : $\mu _r\mu _0n _1n _2\pi r _1^2l$

In the method using the transformers, assume that the ratio of the number of turns in the primary to that in secondary in the step-up transformer is $1:10$. If the power to the consumer has to be supplied at $200\ V$, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is:

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $200:1$

  2. $150:1$

  3. $100:1$

  4. $50:1$

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Correct Option: A

 An inductor of inductance $100\ mH$ is connected in series with a resistance, a variable capacitance and an AC source of frequency $2.0\ kHz$; The value of the capacitance so that maximum current may be drawn into the circuit. 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 50 nF

  2. 60 nF

  3. 63 nF

  4. 79 nF

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Correct Option: C
Explanation:

$\begin{array}{l}{X _L} = Lw = {10^{ - 1}} \times 2\pi  \times 2 \times {10^3}\{X _L} = 4\pi  \times {10^2}\Z = \sqrt {{{\left( {{X _L} - {X _C}} \right)}^2} + {R^2}} \i = \dfrac{V}{Z} = \dfrac{V}{{\sqrt {{{\left( {{X _L} - {X _C}} \right)}^2} + {R^2}} }}\for,{i _{\max }}\{X _L} = {X _C}\\therefore {X _C} = Lw = \dfrac{1}{{Cw}}\C = \dfrac{1}{{{w^2}L}} = \dfrac{1}{{{{10}^{ - 1}} \times 4{\pi ^2} \times 4 \times {{10}^6}}}\ = \dfrac{{{{10}^{ - 5}}}}{{16{\pi ^2}}} = 63nF\end{array}$

$5 \mathrm { mV }$ is induced in a coil, when current in another nearby coil changes by $5 \mathrm { A }$ in $0.1$sec. The mutual inductance between the two coils will be

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $0.1 \mathrm { H }$

  2. $0.2 \mathrm { H }$

  3. $0.1 \mathrm { mH }$

  4. $0.2 \mathrm { mH }$

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Correct Option: A