Question

Two coils P and S have a mutual inductance of 5 x 10^-3 H. If the current in the coil, P is I = 10 sin (100 πt), then the maximum value of the e.m.f. induced in coil S is

• A. 6.28 V
• B. 12.56 V
• C. 15.70 V
• D. 3.14 V

Answer 1

The Correct Option is C

Current in the coil is:
I_p = I₀ sin ωt
Now \(\frac {dI_p}{dt}\) = I₀ω cos ωt
e.m.f = M \(\frac {dI_p}{dt}\)
e.m.f = MIω  cos ωt
Maximum value of the e.m.f. induced in coil: 
e.m.f_max  = 5 x 10^-3 x 10 x 100 πt x1
e.m.f_max =  5 x 10^-3 x 10³ x πt
e.m.f_max = 5π
e.m.f_max  = 5 x 3.14
e.m.f_max  = 15.70 V
Therefore the correct option is (C) 15.70 V.