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 = 10 RC .

Step-by-step solution

The electric current in the circuit is given by i = i₀ e^ -t/RC . The rate of change of current is obtained by differentiating i with respect to time t : di dt = d dt ( i₀ e^ -t/RC ) = i₀ e^ -t/RC ( - 1 RC ) = - i₀ RC e^ -t/RC Substituting t = 10RC into the expression: di dt = - i₀ RC e^ -10RC/RC = - i₀ RC e⁻¹⁰ = - i₀ RCe¹⁰