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 = RC .

Step-by-step solution

Given the electric current i = i₀ e^ -t/RC . The rate of change of current is given by di dt . Differentiating i with respect to t gives: di dt = d dt (i₀ e^ -t/RC ) = - i₀ RC e^ -t/RC Substituting t = RC into the expression: di dt = - i₀ RC e^ -RC/RC = - i₀ RC e⁻¹ = - i₀ RCe