RLC Circuit help

Question

In an RLC circuit:

R = 2 Omega

L = 3 H

C = 8 F

A phasor diagram is drawn for this circuit and it is found that:

the phasor for the inductor is 3 times longer than the phasor for the resistor

the phasor for the capacitor is the same length as the phasor for the resistor

(You will be asked to show this phasor diagram in the file upload)

Find w, the angular frequency of the circuit. Find E0, the amplitude of the voltage of the AC power supply in terms of the voltage on the resistor (In other words, find out how many times longer the E phasor is than the VR phasor).

Your answers:

w = _____ rad/s

E0 = _____ V0R, where V0R is the amplitude of the voltage on the resistor. Please write this as a decimal number.

Answer 1

a) assume R and L and C are connected in series

b) assume when you say "phasor" you mean the voltage vector

c) given a and b and V_L=3V_R and VC=V_R

d) given a,b and c then X_L/X_C=3, thus 3*8w²=3 and thus w=.118 rad/sec

e) XL=.118*3=.354 ohms and XC=1/.118/8=1.06 ohms

f) E_o= I*(2+j.354-j1.06)= 2.12I @angle -71.5 degrees) = 2.12I/2I = 1.06V_R