Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I₀ = 10 A sin ωt, where I₀ = 10 A and ω = 100 π radian/sec. The maximum value of e.m.f. in the second coil is

• A: 2 π
• B: 5 π
• C: π
• D: 4 π

To find the maximum value of the electromotive force (e.m.f.) induced in the second coil due to the changing current in the first coil, we can use the formula for mutual inductance:

Formula for Induced e.m.f.

The induced e.m.f. (ε) in the second coil is given by:

ε = -M (dI₁/dt)

where:

• M = mutual inductance (0.005 H)
• I₁ = current in the first coil

Finding the Derivative of Current

The current in the first coil is given by:

I₁ = 10 A sin(ωt)

To find the rate of change of current (dI₁/dt), we differentiate:

dI₁/dt = 10 A * ω cos(ωt)

Substituting ω = 100π rad/s, we get:

dI₁/dt = 10 A * 100π cos(100πt)

dI₁/dt = 1000π cos(100πt)

Calculating Maximum e.m.f.

The maximum value of cos(100πt) is 1, so:

Maximum dI₁/dt = 1000π

Now substituting this into the e.m.f. formula:

ε = -M (1000π)

ε = -0.005 H * 1000π = -5π V

Final Answer

The maximum value of e.m.f. in the second coil is:

5π

Thus, the correct option is B: 5π.