To solve the circuit variables problem, start by expressing power as the product of current and voltage, P = I * V, using the given functions for v(t) and i(t). Take the derivative of power with respect to time and set it to zero to find critical points, which indicate maximum power. Remember to consider initial conditions, particularly that power is zero for t < 0 due to no current. After finding the time that maximizes power, substitute it back into the power equation to determine the maximum power. The discussion also hints at using the provided information to calculate total power delivered to circuit elements.