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?

Options

A. `(q^(2)ln2)/(3Deltat)R`
B. `(q^(2)ln2)/(4Deltat)R`
C. `(q^(2)ln2)/(Deltat)R`
D. `(q^(2)ln2)/(2Deltat)R`

Answer

D

Explanation

Obviously the current through thhe coil is given by
`i=i_(0)((1)/(2))^((t)/(Deltat))`
Then charge `q=int_(0)^(infty)idt=int_(0)^(infty)i_(0)2^((-t)/(Deltat))dt=(i_(0)Deltat)/(1n2)`
So, `i_(0)=(qln2)/(Deltat)`
And hence heat generated in the circuit in the time interval `t[0,infty]`
`H=int_(0)^(infty)i^(2)Rdt=int_(0)^(infty)[(q1n2)/(Deltat)2^((-t)/(Deltat))]^(2)Rdt=(q^(2)1n2)/(2Deltat)R`