Question

Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate 17.8 A/s, the emf in coil 1 is 27.1 mV. (a) What is their mutual inductance? (b) When coil 2 has no current and coil 1 has a current of 4.00 A, what is the flux linkage in coil 2?

Answer 1

Answer:

Part a)

$M = 1.52 mH$

Part b)

$\phi = 6.09 \times 10^{-3} Tm^2$

Explanation:

Part a)

As we know by Faraday's law

$EMF = M \frac{di}{dt}$

so we will have

$EMF = 27.1 mV$

$EMF = 27.1 \times 10^{-3} V$

$\frac{di}{dt} = 17.8 A/s$

so we will have

$M = \frac{V}{\frac{di}{dt}}$

$M = \frac{27.1 \times 10^{-3}}{17.8}$

$M = 1.52 mH$

Part b)

As we know by Lenz law

$\phi = Mi$

so we have

$\phi = (1.52 \times 10^{-3})(4)$

$\phi = 6.09 \times 10^{-3} Tm^2$