Question

Two coils, held in fixed positions, have a mutual inductance of M = 0.0034 H. The current in the first coil is I(t) = I0sin(ωt), where I0 = 5.4 A, ω = 143 rad/s. Randomized Variables M = 0.0034 H I0 = 5.4 A ω = 143 rad/s show answer No Attempt 25% Part (a) Express the magnitude of the induced emf in the second coil, ε2, in terms of M and I.

Answer 1

Answer:

ε₂ =2.63 V

Explanation:

given,

M = 0.0034 H

I (t) = I₀ sin (ωt)

I (t) = 5.4 sin (143 t)

$\dfrac{d i(t)}{dt} = \dfrac{d}{dt}(5.4 sin (143 t))$

$\dfrac{d i(t)}{dt} =143 \times 5.4 cos (143 t)$

magnitude of the induced emf in the second coil

ε₂ =$M\dfrac{di}{dt}$

ε₂ =$0.0034\times 143 \times 5.4 cos (143 t)$

for maximum emf

cos (143 t) = 1

ε₂ =$0.0034\times 143 \times 5.4$

ε₂ =2.63 V