The circuit shown below is a dc model of a residential power distribution circuit. Use the node – voltage met?
The circuit shown below is a dc model of a residential power distribution circuit. Use the node – voltage method to find the branch currents i1 – i6 .
Test your solution for the branch currents by showing that the power dissipated equals the power developed.
Can someone show me this step-by-step? I'm having a hard time doing this and it's frusterating. I dont know how to solve using node-voltage method. Also, can you also show me how to solve the equations for the voltages?
More Questions From This User See All
Answers & Comments
Verified answer
There are 3 nodes in this circuit. I chose the point between the voltage supplies to be the ground (V=0). V1 is the top of the circuit to the right of the 1 ohm and above the 6. V2 is the midpoint between the 6 and 12 right of the 2 ohm resistor. V3 is the bottom beneath the 12 and right of the 1 ohm resistor.
Next write equations at each node for the sum of the currents leaving that node = 0
V1
(V1-125)/1 + (V1-V2)/6 + (V1-V3)/24 = 0
V2
(V2-V1)/6 + V2/2 + (V2-V3)/12 = 0
V3
(V3-(-125))/1 + (V3-V2)/12 + (V3-V1)/24 = 0
Solving this 3 by 3 is not easy but not impossible.
Use the first eq. to get V1 in terms of V2 and V3
Substitute that into the second equation and get V2 in terms of V3 and substitute both those into the third equation. OR you can setup a matrix:
29 -4 -1 = 3000
-4 18 -2 = 0
-1 -2 27 = -3000
and go to the website in the source. Notice that 125*24=3000
V1 = 101.243V
V2 = 10.657V
V3 = -106.572V
Current in the top 1 ohm = 23.757A to the right
Current in the bottom 1 ohm = 18.428A to the left
Current in the 24 ohm = 8.659A down
These answers check
Residential Power Distribution