You have a resistor of resistance 160 , an inductor of inductance 0.430 H , a ca

Question

You have a resistor of resistance 160 , an inductor of inductance 0.430 H , a capacitor of capacitance 6.50 F and a voltage source that has a voltage amplitude of 31.0 V and an angular frequency of 220 rad/s . The resistor, inductor, capacitor, and voltage source are connected to form an L-R-C series circuit.

Part A

What is the impedance of the circuit?

Z=______________

Part B

What is the current amplitude?

I=_______________A

Part C

What is the phase angle of the source voltage with respect to the current?

=________________      

Part F

What is the voltage amplitude across the inductor?

vL =_____________V

Part G

What is the voltage amplitudes across the capacitor?

vC=______________V

vL =_____________V

Part G

What is the voltage amplitudes across the capacitor?

vC=______________V

Explanation / Answer

R = 160
XL = L = 220*0.43 = 94.6
XC = 1/C = 1/(220*6.5*10^-6) = 699.3
X = |(XL - XC)| = 604.7

Z = sqr(R^2+X^2) = 625.5

I = V/Z = 31/625.5 = 4.95*10^-2 A

current leads voltage
phase angle = arctan(X/R) = 75.18 degrees

Vr = I*R = 4.95*10^-2 A * 160 = 7.93 V
Vl = I*XL = 4.7 V
Vc = I*XC = 34.66 V

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