Question

A battery, capacitor, resistor, and switch are connected as shown. The capacitor is initially uncharged, and the switch is closed at a time t = t_0. Recall that charges cannot flow across the gap between capacitor plates. Just after the switch is closed, what is the potential difference across the resistor and capacitor? Assume the charge on the capacitor at this instant is still zero. In the space below, draw and label separate free-body diagrams for a charge inside the battery and inside the resistor just after the switch is closed. Do any forces on your free-body diagrams above change with time? Describe which forces do, and how they change with time. Does the electric field in the capacitor change with time? If so, how does it change?

How do I do all parts above?

Answer 1

a) just after potential across the capacitor =0

and potential across resistor =V (emf of battery =V)

b) charge inside the capacitor =

V =iR+Q/C (Q =di/dt)

so Q =CV(1- e^-t/RC)

d) so potential difference across capacitor = Q/C=V(1- e^-t/RC)

electric field inside the capacitor =v/d =V(1- e^-t/RC)/d

c) force =QE = CV(1- e^-t/RC)*V(1- e^-t/RC)/d =CV²(1- e^-t/RC)²/d