Question

A resistor with resistance r and a capacitor with capacitance c are connected in series to an ac voltage source. the time-dependent voltage across the capacitor is given by vc(t)=vc0sinωt. part a what is the amplitude i0 of the total current i(t) in the circuit?

Answer 1

Since we are given the voltage over the capacitor, current will be (because resistor and capacitor are in series the current flowing through them has to be the same):
$I=\frac{V_{C0}}{Z_C}$
Where Zc is the impedance of the capacitor. The impedance of the capacitor is:
$Z_C=\frac{1}{Cw}$
When we plug that back into the first formula we get:
$I=\frac{V_{C0}}{1/Cw}=V_{C0}Cw$