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

Step-by-step solution

The current in an RC series circuit during charging is given by I = E R e^ -t/RC . The power converted into heat is the power dissipated across the resistor, which is given by P = I^2 R . Substituting the expression for current, we get: P = ( E R e^ -t/RC )^2 R = E ^2 R e^ -2t/RC The power is maximum when the exponential term e^ -2t/RC is maximum. For t 0 , the maximum value occurs at t = 0 , where e^ -2t/RC = 1 . Therefore, the maximum power converted into heat is: P_ = E ^2 R