At t = 0 , a capacitance C , a resistance R , and an emf E are connected in series. Determine the maximum value of the power delivered by the battery.

Step-by-step solution

The current in a series RC circuit as a function of time is given by: I(t) = E R e^ -t/RC The power delivered by the battery is the product of its emf and the current flowing through the circuit: P(t) = E I(t) = E ^2 R e^ -t/RC Since the exponential term e^ -t/RC is a decreasing function of time for t 0 , the power delivered by the battery is maximum at the initial moment, t = 0 . Substituting t = 0 into the power equation: P_ max = E ^2 R e⁰ = E ^2 R