Question

What amount of heat will be generated in a coil of resistance R due to a charge q passing through it if the current in the coil a. decreases down to zero uniformly during a time interval t_0? b. decrases down to zero having its value every t_0 seconds?

Answer 1

Thus the amount of heat generated will be H = q^2 1n^2  / 2Δt R

Explanation:

Obviously the current through thhe coil is given by

i = i0(1 / 2)^tΔt

Then charge q = ∫∞ - 0 idt = ∫∞ - 0 i02^−t / Δt dt = i0Δt / 1n2

So, i0 = qln2 / Δt

And hence heat generated in the circuit in the time interval t[0,∞]

H=∫∞ - 0 i^2 R dt

H = ∫∞ - 0 [q1n2 / Δt 2^−t / Δt]^2

H = Rdt = q^2 1n^2  / 2Δt R

Thus the amount of heat generated will be H = Rdt = q^2 1n^2  / 2Δt R