Question

What amount of heat will be produced in a coil of resistence r due to a total charge q passing through it if a current in the coil decrease down to zero

Answer 1

Answer:

Current I =dQ/dt Therefore if Q=at-bt^2

I = a-2bt Power produced is I^2 × R

P = a^2+4b^2 t^2 -4abt If you want to calculate total energy or heat produced you have to integrate P with respect to time t applying the limits from 0 to t.

Total energy = a^2×t +4(b^2)(t^3/3)-2ab(t^2)

Explanation:

Answer 2

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