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

Question

Two coils have mutual inductance 0.005 H. The current changes in the first coil according to equation I=I0 sin ω t, where I0=10 A and ω=100 π rad / s. The maximum value of emf in the second coil is (A) 12 π (B) 8 π (C) 5 π (D) 2 π

Tardigrade Admin · Accepted Answer

The instantaneous current in the AC circuit is given by I=I0 sin ω t (d I/d t)=(d/d t)(I0 sin ω t) (d I/d t)=(I0 cos ω t) ω Substituting I0=10 A , w =100 π cos (100 x)=1 we get (d I/d t)=1000 x Hence, induced emf is given by B=M (d I/d t) On putting M=0.005 H , (d I/d t)=1000 π, we get B=(5 π) V

Q. 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

$12 π$

$8 π$

$5 π$

$2 π$

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

12π

8π

5π

2π

The instantaneous current in the AC circuit is given by I=I0​sinωt dtdI​=dtd​(I0​sinωt) dtdI​=(I0​cosωt)ω Substituting I0​=10A,w=100π cos(100x)=1 we get dtdI​=1000x Hence, induced emf is given by B=MdtdI​ On putting M=0.005H,dtdI​=1000π, we get B=(5π)V

Q. 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

$12 π$

$8 π$

$5 π$

$2 π$