In a discharging R – C circuit, the electric current is given by i = i₀ e^ -t/RC , where i₀ , R and C denote constant parameters and t represents time. If i₀ = 2.00 A , R = 6.00 10^5 and C = 0.500 F , ascertain the rate of change of current at t = 0.3 s .

Step-by-step solution

Given i = i₀ e^ -t/RC The rate of change of current is given by: di dt = d dt (i₀ e^ -t/RC ) = - i₀ RC e^ -t/RC Substituting the given values: R = 6.00 10^5 C = 0.500 10⁻⁶ F RC = (6.00 10^5) (0.500 10⁻⁶) = 0.3 s At t = 0.3 s : di dt = - 2.00 0.3 e^ -0.3/0.3 = - 20 3 e⁻¹ = - 20 3e A/s