The electric curren in a charging R-C circuit is given by `i=i_0e^(-t/RC)` when `i_0`, R and C aere constant parameters of the circuit and t is time. Find the rate of change of current at `a. t=0, b. t=RC c. t=10RC`.

Answer

(a)-i/RC (b)-i/Rce (c)-i/Rcxe^10

Explanation

Given that, `i =i_0e^(-t/RC), Rate of change of current
= di/dt=i_0((-1)/(RC))e^(-t/RC)
=(-i_0)/(RC)xxe^(-t/RC)
when a. t=0
di/dt=(-i_0)/Rcxe^0=(-i_0)/RC
b. t=RC, di/dt=(-i_0)/Rcxe^(-1)=(-i_0)/(Rce)
c. t=10, di/dt=(-i_0)/Rcxe^10`