How many time constants will elapse before the current in a charging RC circuit decreases to half of its initial value? Answer the same question for a discharging RC circuit.

Step-by-step solution

For a charging RC circuit, the current at any time t is given by i = i₀ e^ -t/ , where = RC is the time constant and i₀ is the initial current. We are given that the current decreases to half of its initial value, so i = i₀ 2 . i₀ 2 = i₀ e^ -t/ e^ t/ = 2 t = 2 0.693 t 0.69 For a discharging RC circuit, the current at any time t is also given by i = i₀ e^ -t/ . Similarly, for the current to decrease to half of its initial value, i = i₀ 2 . i₀ 2 = i₀ e^ -t/ e^ t/ = 2 t = 2 0.693 t 0.69 Thus, in both cases, 0.69 time