This is an example of circuit analysis using the nodal method. Solve the circuit below:
Calculation Procedure
1. Label the Circuit
Label all nodes (Fig. 1.12). One of the nodes (node A) is chosen as the reference node. It can be thought of as a circuit ground, which is at zero voltage or ground potential.
Nodes B and D are already known to be at the potential of the source voltages. The voltage
at node C (VC) is unknown.
Assume that VC VB and VC VD. Draw all three currents I1, I2, and I3 away from node C, that is, toward the reference node.
2. Write KCL at Node C
I1 + I2 + I3= 0.
3. Express Currents in Terms of Circuit Voltages Using Ohm’s Law
Refer to Fig. 1.12: I1= V1/R1= (VC - 8)/2, I2= V2 /R2= (VC - 24)/1, and I3= V3 /R3= VC/4.
4. Substitute in KCL Equation of Step 2
Substituting the current equations obtained in Step 3 into KCL of Step 2, we find I1 + I2 + I3= 0 or (VC - 8)/2 + (VC - 24)/1 + VC/4= 0.
Because the only unknown is VC , this simple equation can be solved to obtain VC= 16 V.
5. Solve for All Currents
I1= (VC - 8)/2= (16 - 8)/2= 4 A (true direction) and I2= (VC - 24)/1= (16 -24)/1 = -8 A. The negative sign indicates that I2 flows toward node C instead of in the assumed direction (away from node C). I3= VC/4= 16/4= 4 A (true direction).
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