In a charging R – C circuit, the electric current is given by i = i₀ e^ -t/RC , where i₀ , R , and C are constant parameters of the circuit and t represents time. Determine the rate of change of current at t = 0 .

Step-by-step solution

Given the electric current i = i₀ e^ -t/RC . The rate of change of current is given by the derivative of i with respect to time t : di dt = d dt ( i₀ e^ -t/RC ) di dt = i₀ e^ -t/RC ( - 1 RC ) = - i₀ RC e^ -t/RC To find the rate of change of current at t = 0 , substitute t = 0 into the expression: . di dt |_ t=0 = - i₀ RC e⁰ = - i₀ RC