The RMS phasor current drawn by the total load is 10.3 - j4.6 Amps. Option C is the right choice.
To find the RMS phasor current drawn by the total load, we can first calculate the complex impedance of each load and then add them up using the parallel rule. Then, we can divide the source voltage by the total impedance to get the current.
Calculate the complex impedance of each load:
Load 1: 820-j242 VA / 120 VRMS = 6.83-j2.02 Ω
Load 2: 404+j782 VA / 120 VRMS = 3.37+j6.52 Ω
Add the complex impedances using the parallel rule:
1/(6.83-j2.02 Ω + 3.37+j6.52 Ω) = (0.118+j0.034) Ω
Divide the source voltage by the total impedance:
120 VRMS / (0.118+j0.034) Ω = 1004-j340 VRMS/Ω
Take the magnitude of the current:
|1004-j340 VRMS/Ω| = 1030 VRMS/Ω
Convert the magnitude and angle to RMS phasor notation:
1030 VRMS/Ω * cos(-atan2(340, 1004)) - j * 1030 VRMS/Ω * sin(-atan2(340, 1004))
= 10.3 - j4.6 Amps
Option C is the right choice.
Question:-
Loads shown in the circuit are connected in parallel and served by an AC Voltage Source. Find the RMS Phasor Current drawn by the Total Load.
A. 10.5 - j4.8 Amps
B. 10.4 - j4.7 Amps
C. 10.3 - j 4.6 Amps
D. 10.2 - j4.5 Amps
E. 10.1 - j4.4 Amps