In the circuit shown below, E = 20 V RMS L 70 degrees, R = 20 ohms, XL = 20 ohms

Question

In the circuit shown below, E = 20 V RMS L 70 degrees, R = 20 ohms, XL = 20 ohms, and XC = 60 ohms A.) Calculate the RMS voltage drop across the inductor, V1 (do not include phase angle here): ___ volts RMS
B.) Calculate the phase angle of the voltage drop across the inductor, V1 (do not include voltage drop value here, just its angle): ___ degrees
C.) Calculate the RMS voltage drop across the capacitor, V2 (do not include phase angle here): ___ volts RMS
D.) Calculate the phase angle of the voltage drop across the capacitor, V2 (do not include voltage drop value here, just its angle): ___ degrees

Explanation / Answer

1) using voltage divider :

V1 = [j20 / (20 + j20 - j60)] x 20 < 70

=> V1 = [j20 / (20 - j40)] x (6.84 + j18.8)

=> V1 = (- 376 + j136.8) / (20 - j40)

=> V1 = (400.11 < 160o ) / (44.72 < -63.43o )

=> V1 = 8.95 < 223.43o V

so ,

A) V = 8.95 V

B) angle = 223.43o

2) in the same way :

V2 = [-j60 / (20 + j20 - j60)] x 20 < 70

=> V1 = [-j60 / (20 - j40)] x (6.84 + j18.8)

=> V1 = (1128 - j410.4) / (20 - j40)

=> V1 = (1200.33 < -20o ) / (44.72 < -63.43o )

=> V1 = 26.8 < 43.43o V

so ,

C) V = 26.8 V

D) angle = 43.43o

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