$$ A circuit has an ac voltage source and a resistor and capacitor connected in series. There is no inductor. The ac voltage source has voltage amplitude $900$ V and angular frequency $.$ The voltage amplitude across the capacitor is $500$ V$.$ The resistor has resistance $.($a$)$ What is the voltage amplitude across the resistor? $($b$)$ What is the capacitance of the capacitor? $($c$)$ Does the source voltage lag or lead the current? $($d$)$ What is the average rate at which the ac source supplies electrical energy to the circuit?