Construct an electrical circuit to find the values of Xa, Xb, and Xc in this system of equations:
21Xa – 10Xb – 10Xc = 1
–10Xa + 22Xb – 10Xc = –2
–10Xa – 10Xb + 20Xc = 10
Your circuit should include only the following elements:
- one 1Ω resistor
- one 2Ω resistor
- three 10Ω resistors
- three ideal constant voltage sources
- three ideal ammeters
The circuit should be designed such that each ammeter displays one of the values, Xa, Xb and Xc.
What do the coefficients on the left side of the equations represent? What about the constants on the right side?
The coefficients on the left side of each equation represent resistances. Resistance multiplied by current (the unknown Xa, Xb and Xc values) yields voltage.
The “bare” numbers on the right side of each equation represent voltages directly; i.e., independent voltage sources.