A resistor, R = 100 Ω, an inductor, L = 0.20 H and a capacitor, C = 3 µF are connected in series across an ac source of VS = 100 V and frequency, f = 200 Hz. Calculate the following for this series circuit:
a) the total circuit impedance (Zt)
b) the total circuit current (IS)
c) the voltage drop across each component (VR, VL and VC)
d) the phase angle between VS and It.
e) Draw the phasor diagram of voltages and current for the circuit.
f) What is the frequency of the ac source for maximum current to flow?
g) What is the quality factor, Q, of the circuit at the frequency calculated in part f)?
The Attempt at a Solution
R = 100 ohms
L = 0.2 henries
C = 3*10^-6 farads
Vrms = 100V therefore Vmax = 100*sqrt2 = 141.42
freq = 200Hz therefore w = 1256.64
Z = sqrt[(R^2 + (XL-Xc)^2] = 100.97
Irms = Vrms/Z = 0.99 therefore Imax = 0.99*sqrt2 = 1.4
now here is where im stuck... the voltage drop...
Voltage drop across resistor, VR = R*Imax = 140V
Voltage drop across inductor, VL = XL*Imax = 352.03
Voltage drop across capacitor, VC = Xc*Imax = 371.51
and kirchoff says Vmax^2 = VR^2 + (VL-VC)^2
subbing in... Vmax = 74.16 which is wrong... since Vmax = 141.42