EBK MINDTAP FOR HERMAN'S DELMAR'S STAND
EBK MINDTAP FOR HERMAN'S DELMAR'S STAND
7th Edition
ISBN: 9781337900614
Author: Herman
Publisher: VST
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Chapter 22, Problem 2PP
To determine

The missing values in the table.

Expert Solution & Answer
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Answer to Problem 2PP

ET = 54 V ER = 54 V EC = 54 V
IT = 2.5 A IR = 1.5 A IC = 2 A
Z = 21.6 Ω R = 36 Ω XC = 27 Ω
VA = 135 P = 81 W VARSC = 108
PF = 60 % ∠θ =53.13 ° C =14.736 µF

Explanation of Solution

Given data:

IC=2A  f=400 Hz  R = 36 Ω  Z = 21.6 Ω

The capacitive reactance XC is calculated as,

1Z2=1R2+1XC21XC2=1Z21R21XC2=121.6213621XC2=1466.56112961XC2=1296466.561296×466.561XC2=829.44604661.76Invert the ratio,XC2=604661.76829.44XC2=729Taking square root,XC=729     =27Ω

The value of the capacitor is,

C=12πfXc=12π×400×27=14.736 μF

The voltage drop across the capacitor,

EC=ICXC    =2×27    =54V

Since the circuit is parallel R-C,

EC=ER=ET=54 V

The current flowing through resistance IR will be,

IR=ERR=5436=1.5 A

The total current flowing in the parallel R-C network is,

IT=ETZ=5421.6=2.5 A

The apparent power VA is given as,

VA=ETIT    =54×2.5    =135

The true power P is given as,

P=ERIR    =54×1.5    =81 W

The reactive power VARSC is calculated as,

VARSC  = VA2P2             =1352812             = 108

Power factor (PF) is calculated as,

PF=PVA×100     =81135×100     =60 %

Power factor angle θ will be,

cosθ=0.6     θ=cos10.6     θ=53.13°

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