Tag: electromagnetic induction and alternating currents

Questions Related to electromagnetic induction and alternating currents

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:

Mutual inductance M=$\sqrt{ L _1\times L _2}=\sqrt{ 2\times 8}=4$mH

Mutual inductance of a system of two thin coaxial conducting loops of radius each, their centers separated by distance $d (d >>r)$ is 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\mu _0\pi r^4d^3$

  2. $\dfrac{\mu _0\pi r^4}{2d^3}$

  3. $\dfrac{\mu _0\pi r^4}{d^3}$

  4. $\dfrac{\mu _0\pi r^4 d^3}{4}$

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Correct Option: B

The coefficient of mutual inductance, when magnetic flux changes by $\displaystyle 2\times { 10 }^{ -2 }Wb$ and current changes by 0.01 A is :

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 8 henry

  2. 4 henry

  3. 3 henry

  4. 2 henry

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Correct Option: D
Explanation:

We know that

$\displaystyle \phi =Mi$
$\displaystyle d\phi =Mdi$

$\displaystyle M=\frac { d\phi  }{ di } =\frac { 2\times { 10 }^{ -2 } }{ 1\times { 10 }^{ -2 } } =2$ henry