An emf of 20 V is applied at time $t=0$ to a circuit containing in series 10 mH inductor and $5 \Omega$ resistor. The ratio of the currents at time $t=\infty$ and at $t=40$ s is close to: (take $e^{2}=7.389$)

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Electromagnetic Induction

An emf of 20 V is applied at time

t = 0

to a circuit containing in series 10 mH inductor and

5Ω

resistor. The ratio of the currents at time

t = \infty

and at

t = 40

s is close to: (take

e^{2} = 7.389

)

(A)1.06
(B)0.84
(C)1.46
(D)1.15✓ Correct

Answer: (D)

Solution

For an

R L

circuit the growing current is

i (t) = i_{0} (1 - e^{- t / τ})

with

i_{0} = V / R

and

τ = L / R

. The required ratio is

\frac{i ( \infty )}{i ( t )} = \frac{1}{1 - e ^{- t / τ}}

. Using the supplied data (

t / τ = 2

e^{2} = 7.389

\frac{1}{1 - e ^{- 2}} = \frac{e ^{2}}{e ^{2} - 1} = \frac{7.389}{6.389} \approx 1.15

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option

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