All new homes are required to install a device called a ground fault circuit interrupter

QUESTION:

All new homes are required to install a device called a ground fault circuit interrupter (GFCI) that will provide protection from shock. By monitoring the current going to and returning from a receptacle, a GFCI senses when normal flow is interrupted and switches off the power in 1 / 40 second. This is particularly important if you are holding an appliance shorted through your body to ground. A circuit model of the GFCI acting to interrupt a short is shown in Figure P 14.7-19. Find the current flowing through the person and the appliance, i(t), for t \(\geq\) 0 when the short is initiated at t = 0. Assume v = 160 \cos 400 t and the capacitor is intially uncharged.