Question

An emf of 15 V is applied in a circuit containing 5H inductance & 10Ω resistance. The ratio of the currents at  time t = ∞ and at t = 1sec.

(a) [{e^(1/2)}/{e^(1/2) – 1}]

(b) 1 – e^–1

(c) [{e²}/{e² – 1}]

(d) e^–1

Answer 1

The correct option (c) [{e²}/{e² – 1}]

Explanation:

e = 15V

L = 5H

R = 10Ω

current = I = I_O(1 – e^–(Rt/L))

at t = ∞,   I = I_O(1 – e^–∞) = I_O(1 – 0) = I_O

at t = 1,  I = I_O(1 – e^–(R/L))

Hence

[{I_t=∞sec} / {I_t=1sec}]  = [{I_O}/{I_O(1 – e^–(R/L))}]

= [1/{1 – e^–(R/L)}]

= [1/{1 – e^–(10/5)}]

∴ ratio is [1/{1 – e^–2}] = [1/{1 – (1/e²)}] = [{e²}/{e² – 1}].