Problem 24.22 A 65.0 Hz generator with an rms voltage of 105 V is connected in s

Question

Problem 24.22

A 65.0 Hz generator with an rms voltage of 105 V is connected in series to a 3.40 k resistor and a 1.00 Fcapacitor.

Part A

Find the rms current in the circuit.

10.45

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Part B

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

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Problem 24.22

A 65.0 Hz generator with an rms voltage of 105 V is connected in series to a 3.40 k resistor and a 1.00 Fcapacitor.

Part A

Find the rms current in the circuit.

Irms =

10.45

  mA  

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Incorrect; Try Again; 5 attempts remaining

Part B

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

= degrees

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Explanation / Answer

f = 65 Hz ; Vl = 105 V ; R = 3400 Ohm ; C = 1 uF

a)We know that,

Z = sqrt (R^2 + Xc^2) = sqrt (R^2 + (1/wC)^2)

Z = sqrt (3400^2 + 1/2 x 3.14 x 65 x 10^-6)^2 = 4190.63 Ohm

Irms = Vrms/Z

Irms = 105/4190.63 = 0.025 A

Hence, Irms = 0.025 A = 25 mA

b)phase angle will be:

phi = cos-1 (R/Z)

phi = cos-1 (3400/4190.63) = 35.77 deg

Hence, phi = 35.77 deg

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