At t = 0 , a capacitance C , a resistance R , and an emf E are connected in series. Determine the maximum value of the energy stored in the capacitor.

Step-by-step solution

The charge on the capacitor at any time t during the charging of an RC circuit is given by: q(t) = C E (1 - e^ -t/RC ) The energy stored in the capacitor at any time t is: U(t) = q(t)^2 2C The maximum charge on the capacitor is reached in the steady state as t : q_ max = C E Substituting the maximum charge into the energy formula, the maximum energy stored in the capacitor is: U_ max = q_ max ^2 2C = (C E )^2 2C = 1 2 C E ^2