Problem 24.22 A 50.0Hz generator with an rms voltage of 110V is connected in ser

Question

Problem 24.22

A 50.0Hz generator with an rms voltage of 110V is connected in series to a 3.65k? resistor and a 2.50?F capacitor.

Part A

Find the rms current in the circuit.

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Part B

Find the phase angle, ?, between the current and the voltage.

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Problem 24.22

A 50.0Hz generator with an rms voltage of 110V is connected in series to a 3.65k? resistor and a 2.50?F capacitor.

Part A

Find the rms current in the circuit.

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Part B

Find the phase angle, ?, between the current and the voltage.

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Explanation / Answer

a)

Capacitive reactance

Xc=1/2pifC =1/2pi*50*(2.5*10-6)

Xc=1273.2 ohms

Impedance

Z=sqrt[R2+Xc2]=[36502+1273.22]

Z=3865.7 ohms

Rms current

Irms =Vrms/Z =110/3865.7

Irms=28.46 mA

b)

phase angle

o=tan^-1(-Xc/R)=tan^-1(-1273.2/3650)

o=19.2 degrees

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