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

Answer: (C)

15.70 V

Answer 2

Current in the coil is:
Ip = 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.fmax = 5 x 10-3 x 10 x 100 πt x1
e.m.fmax = 5 x 10-3 x 103 x πt
e.m.fmax = 5π
e.m.fmax = 5 x 3.14
e.m.fmax = 15.70 V
Therefore the correct option is (C) 15.70 V.