# RC Circuit

A constant voltage  is applied to the circuit shown which contains two resistors, a multi-way switch and  a capacitor. Initially open, the switch is closed to the left for a time  and then closed to the right for a further time , before being set to open. Express the voltage  across the capacitor as a function of time.
In the first phase  with the switch to the left we have a charging RC circuit At the end of this time the charge on the capacitor is . This forms the initial charge for the second phase  with the switch to the right. This is now a discharging RC circuit. Note that we have used  because time in this section is running from  to . Use the interactivity below to investigate how the final Voltage on the capacitor varies with , ,  and .