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Question

The magnetic field at a point inside a 2.0 mH inductor-coil becomes 0.80 of its maximum value in 20 µs when the inductor is joined to a battery. Find the resistance of the circuit.

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Solution

Given:
Inductance of the inductor, L = 2.0 mH
Let the resistance in the circuit be R and the steady state value of the current be i0.
At time t , current i in the LR circuit is given by
i = i0(1 − e−t)
Here,
τ=LR = Time constant
On multiplying both sides by µ0n, we get
n = Number of turns per unit length of the coil
µ0ni = µ0ni0(1 − et)
⇒ B = B0(1 − e−tR/L)
⇒ 0.8 B0 = B01-e-20×10-6R2×10-3
⇒ 0.8 = (1 − e−R/100)
⇒ e−R/100 = 0.2
⇒ ln (eR/100) = ln (0.2)
-R100 = −1.693
⇒ R = 169.3 Ω

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