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

Answer

C

Explanation

As current I is function of time and at `t=0` and `Deltat`, it equal `i_(0)` and zero respectively it may be represented as, `i=i_(0)(1-(t)/(Deltat))`
Thus `q=int_(0)^(Deltat)idt=int_(0)^(Deltat)i_(0)(1-(t)/(Deltat))dt=(i_(0)Deltat)/(2)`
so, `i_(0)=(2q)/(Deltat)`
The heat generated
`H=int_(0)^(Deltat)i^(2)Rdt=int_(0)^(Deltat)[(2q)/(Deltat)(1-(t)/(Deltat))]^(2)Rdt=(4q^(2)R)/(3Deltat)`