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/τ)
Here,
= Time constant
On multiplying both sides by µ0n, we get
n = Number of turns per unit length of the coil
µ0ni = µ0ni0(1 − e−t/τ)
⇒ B = B0(1 − e−tR/L)
⇒ 0.8 B0 = B0
⇒ 0.8 = (1 − e−R/100)
⇒ e−R/100 = 0.2
⇒ ln (e−R/100) = ln (0.2)
⇒ = −1.693
⇒ R = 169.3 Ω