You have a resistor of resistance 210? , an inductor of inductance 0.410H , a ca

Question

You have a resistor of resistance 210? , an inductor of inductance 0.410H , a capacitor of capacitance 6.10?F and a voltage source that has a voltage amplitude of 31.0V and an angular frequency of 260rad/s . The resistor, inductor, capacitor, and voltage source are connected to form an L-R-C series circuit.

a)What is the impedance of the circuit?

b) What is the current amplitude?

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

d)Does the source voltage lag or lead the current?

e)What is the voltage amplitude across the resistor?

f)What is the voltage amplitude across the inductor?

g)What is the voltage amplitudes across the capacitor?

h)What is the voltage amplitudes across the capacitor?

Thanks in advance!

Explanation / Answer

a)

Inductive reactance

XL=WL=260*0.41 =106.6 ohms

Capacitive reactance

Xc=1/WC =1/260*(6.1*10-6)=630.5 ohms

Impedance

Z=sqrt[R2+(XL-Xc)2]=sqrt[2102+(106.6-630.5)2]

Z=564.4 ohms

b)

Voltage amplitude

I=V/Z =31/564.4

I=0.05492 A

c)

Phase angle

o=tan-1(XL-Xc/R) =tan-1(106.6-564.4/210)

o=-65.36o

d)

Voltage lag current

e)

VR=I*R =0.05492*210 =11.53 Volts

f)

VL=IXL=0.05492*106.6=4.85 Volts

g)

VC=IXc=0.05492*630.5 =34.63 Volts

h)

Vc=34.63 Volts

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