A conductor has a temperature independent resistance `R` and a total heat capacity `C`. At the moment `t=0` it is connected to a `DC` voltage `V`. Find the times dependence of the conductors temperature t assuming the thermal power dissipated into surrounding space to vary as `q=k(T-T_0)` where `k` is a constant `T_0` is the surrounding temperature (equal to conductor's temperature at the initial moment).

Answer

A, B, C

Explanation

`V^2/R=k(T-T_0)+C((dT)/(dt))`
or `(dT)/(V^2/R-k(T-T_0))=(dt)/C`
`or int_(T_0)^T(dT)/(V^2/R-k(T-T_0))=int_0^1(dt)/C`
(at t=0 temperature of conductor `T=T_0)`
Solving this equation we get
`T=T_0+V^2/(kR)(1-e^(-kt//C))`