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

Correct Answer - `4/3(q^(2)R)/(Deltat)`
`H=int_(0)^(Deltat)I^(2)Rdt....(1)`
`q=int_(0)^(Deltat)Idt...(2)`
`I=I_(0)-(I_(0))/(Deltat)t....(3)`
From `(2)` and `(3)` `q=int_(0)^(Deltat)(I_(0)-(I_(0))/(Deltat)t)dt`
`q=(I_(0)Deltat)/2implies I_(0)=(2q)/(Deltat)....(4)`
From `(1)` and `(3)` `H=int_(0)^(Deltat)(I_(0)-(I_(0))/(Deltat)t)^(2) Rdt`
`H=(I_(0)^(2)RDeltat)/3`
putting the value of `I_(0)` from equation `(4)` `H=(4q^(2)R)/(3Deltat)`