Question

JEE MAINS PHYSICS QUESTION SEPTEMBER 2020

Answer 1

The circuit on at t = 0, find the time when energy speed in inductor becomes 1/n times of maximum energy stored in it.

solution : energy stored in inductor is given by, U = 1/2 Li²

here inductance L remains constant

so, U ∝ I²

i.e., U₁/U₂ = (I₁/I₂)²

here let U₂ = U₀ = maximum energy stored in inductor

so, U₁/U₂ = 1/n

we know, I = I₀[1 - e¯Rτ/L ]

so, I₁ = I₂ [1 - e¯Rτ/L] [ as I₂ = I₀]

⇒I₁/I₂ = (1 - e¯Rτ/L)

so, 1/n = (1 - e¯Rτ/L)²

⇒1/√n = (1 - e¯Rτ/L)

⇒(√n - 1)/√n = e¯Rτ/L

⇒ln[(√n - 1)/√n] = -Rτ/L

⇒Lln[√n/(√n - 1)] = Rτ

but τ = (L/R) ln [√n/(√n - 1) ]

Therefore time when energy speed in inductor becomes 1/n times of maximum energy stored in it is (L/R) ln [√n/(√n - 1) ]