Question

An RLC series circuit has a 2.50 Ω resistor, a 100 µH inductor, and an 87.5 µFcapacitor.

(a)

If the voltage source is Vrms = 5.60 V , what is the Irms at 120 Hz?

A ( ± 0.001 A)

(b)

What is the phase angle of the current vs voltage at this frequency? Enter a positive number between 0 and 90

degrees ( ± 0.1 degrees)

(c)

What is the Irms at 5.0 kHz?

A ( ± 0.01 A)

(d)

What is the phase angle of the current vs voltage at this frequency? Enter a positive number between 0 and 90

degrees ( ± 0.1 degrees)

(e)

What is the resonant frequency of the circuit?

kHz ( ± 0.01 kHz)

(f)

What is Irms at resonance?

A ( ± 0.01 A)

(g)

What is the phase angle of the current vs voltage at resonance? Enter a positive number between 0 and 90

degrees ( ± 0.1 degrees)

Answer 1

resistance R=2.5 ohms

inductance L=100*10^-6 H

capacitance C=87.5*10^-6 F

a)

Vrms=5.6 v

f=120 Hz

===> w=2pif=2pi*120 = 753.98 rad/sec

Imax=Vmax/sqrt(R^2+(wL-1/wC)^2)

Imax=Vrms*sqrt(2)/sqrt(R^2+(wL-1/wC)^2)

Irms=Imax/sqrt(2) =vrms/(sqrt(R^2+(wL-1/wC)^2))

Irms=5.6/(sqrt(2.5^2+(753.98*100*10^-6-1/(753.98*87.5*10^-6))^2)

Irms=0.36 A

b)

tan(theta)=(WL-1/WC)/R

tan(theta)=(753.98*100*10^-6-1/(753.98*87.5*10^-6))/2.5

theta=80.6 degrees

c)

f=5 kHz =5*10^3 Hz

===> w=2pif=2pi*5*10^3 = 31.41*10^3 rad/sec

Irms=Imax/sqrt(2) =vrms/(sqrt(R^2+(wL-1/wC)^2))

Irms=5.6/(sqrt(2.5^2+(31.41*10^3*100*10^-6-1/(31.41*10^3*87.5*10^-6))^2)

Irms=1.5 A

d)

tan(theta)=(WL-1/WC)/R

tan(theta)=(31.41*10^3*100*10^-6-1/(31.41*10^3*87.5*10^-6))/2.5

theta=48 degrees

e)

resonace frequency f=1/2pi*sqrt(LC)

f=1/(2pi*sqrt(100*10^-6*87.5*10^-6))

f=1701.44 Hz

f)
at resonance,

Irms=Vrms/R

Irms=5.6/2.5

Irms=2.24 A

g)

tan(theta)=(WL-1/WC)/R

tan(theta)=0

===> theta=0 degrees