Two coils have mutual inductance 0-005 H- The current changes in the first coil according to equation I- I 0 sin- t- where I 0 -10 A and - -100- rad - s- The maximum value of emf in the second coil is

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Inductors in Circuits

Two coils hav...

Question

Two coils have mutual inductance $0.005 H$ . The current changes in the first coil according to equation $I = I_{0} sin ω t$ , where $I_{0} = 10 A$ and $ω = 100 π r a d / s$ . The maximum value of emf in the second coil is

12 π

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8 π

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5 π

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2 π

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Solution

The correct option is C $5 π$
The instantaneous current in the AC circuit is given by $I = I_{0} sin ω t$
$\frac{d I}{d t} = \frac{d}{d t} (I_{0} sin ω t)$
$\frac{d I}{d t} = (I_{0} cos ω t) ω$
Substituting $I_{0} = 10 A$ , $ω = 100 π$
$cos (100 π) = 1$ , we get
$\frac{d I}{d t} = 1000 π$
Hence, induced emf is given by
$E = M \frac{d I}{d t}$
On putting $M = 0.005 H$ , $\frac{d I}{d t} = 1000 π$ , we get
$E = (5 π) V$

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Two coils have mutual inductance 0.005H. The current changes in the first coil according to equation I=I0sinωt, where I0=10A and ω=100πrad/s. The maximum value of emf in the second coil is

The correct option is C 5πThe instantaneous current in the AC circuit is given by I=I0sinωtdIdt=ddt(I0sinωt)dIdt=(I0cosωt)ωSubstituting I0=10A, ω=100πcos(100π)=1, we getdIdt=1000πHence, induced emf is given byE=MdIdtOn putting M=0.005H, dIdt=1000π, we getE=(5π)V

Two coils have mutual inductance $0.005 H$ . The current changes in the first coil according to equation $I = I_{0} sin ω t$ , where $I_{0} = 10 A$ and $ω = 100 π r a d / s$ . The maximum value of emf in the second coil is