The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The ca

Question

The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The capacitive and inductive reactances are 940 and 330 , respectively. The resistance is 490 . In the figure, the resistance is changed from its original value so that the power factor is now 0.80. The original values of capacitance, inductance, and frequency remain unchanged. The new resistance is closest to:

The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The capacitive and inductive reactances are 940  and 330 , respectively. The resistance is 490 . In the figure, the resistance is changed from its original value so that the power factor is now 0.80. The original values of capacitance, inductance, and frequency remain unchanged. The new resistance is closest to:

Explanation / Answer

theta be the angle b/w instantaneous current and voltage

tan theta = ( XL - XC) /R

tan(theta) = ( 940 - 330 ) /R

power factor = cos(theta)

cos(theta) = .8

theta = 0.643501109 radians

tan(0.643501109) = 0.75

=> ( 940 - 330 ) /R = 0.75

R = 813.33 ohm

closest to 810

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