Question

An R-C circuit is driven by an alternating voltage of amplitude 110 and frequency . Define to be the amplitude of the voltage across the capacitor. The resistance of the resistor is 1000 , and the capacitance of the capacitor is 1.00 . I need help on what to do I'm lost thanks.

Answer 1

Vc = Q/C
Vr = i R
V = Vc+Vr if in series

here i = I cos wt
Q = integral idt = (I/w) sin wt

Vc = (I/wC) sin wt
Vr = IR cos wt
so
V = I [ (1/wC) sin wt + R cos wt ]
but
given V = 110 sin(wt+P) where P is some phase angle
Trig identity
V = 110 [ sin wt cos P + cos wt sin P]
so
110 cos P = I/wC and 110 sin P = IR
110^2 cos^2 P = (I/wC)^2
110^2 sin^2 P = (IR)^2
add
110^2 (1) = I^2 [(1/wC)^2 + R^2 ]
so
If you know w, C and R
you can get I right there
Now you want Vc ?
we know Vc = (I/wC) sin wt
we know I, w and C so we know the amplitude of Vc