In an RC circuit, how many time constants must elapse before the power delivered by the battery decreases to half of its maximum value?

Step-by-step solution

The power delivered by the battery in an RC circuit is given by P = VI , where V is the constant voltage of the battery and I is the current. The current in a charging RC circuit as a function of time is I = I₀ e^ -t/ , where I₀ is the maximum current at t = 0 and is the time constant. Substituting the expression for current, the power delivered by the battery is: P = V I₀ e^ -t/ = P_ e^ -t/ We need to find the time t when the power decreases to half of its maximum value, so P = P_ 2 . P_ 2 = P_ e^ -t/ e^ -t/ = 1 2