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 , calculate approximately the current at t = 0.31 s .

Step-by-step solution

The time constant of the circuit is given by = RC . Substituting the given values: = (6.00 10^5) (0.500 10⁻⁶) = 0.30 s The current at time t is given by: i = i₀ e^ -t/RC Substituting i₀ = 2.00 A and t = 0.31 s : i = 2.00 e^ -0.31/0.30 = 2.00 e^ -31/30 This can be rewritten as: i = 2.00 e⁻¹ e^ -1/30 Using the approximation e^ -x 1 - x for small x , we get e^ -1/30 1 - 1 30 = 29 30 . Therefore, the current is approximately: i 2.00 e ( 29 30 ) = 58 30e = 5.8 3e A