When using node-voltage analysis with a voltage source connected between two non-reference nodes, what technique is commonly used?

When using node-voltage analysis with a voltage source connected between two non-reference nodes, what technique is commonly used?

• A. Ignore the voltage source and apply standard KCL at each node.
• B. Use a supernode around the two nodes and write KCL for the supernode only, without a constraint.
• C. Write KCL at one node and ignore the other node connected by voltage source.
• D. Use a supernode around the two nodes and write KCL for the supernode plus a constraint equation from the voltage source.

Answer: (D)

When a voltage source sits between two non-reference nodes, you can’t write independent KCL equations at each node because the current through that source is unknown. The standard approach is to enclose both nodes with a single supernode and write KCL for that entire supernode, summing currents leaving through all elements connected to either node while excluding the current through the voltage source itself. Then you add a constraint equation that expresses the fixed voltage difference imposed by the source between the two nodes. This constraint links the two node voltages, so together with the supernode KCL you obtain solvable equations for the node voltages. If the voltage source were connected to the reference node, you could simply set the corresponding node voltage to the source value and proceed without a supernode. The other options fail because they either ignore the voltage source’s presence, treat only one node, or omit the necessary voltage-relationship constraint, leaving the system underdetermined.

When a voltage source sits between two non-reference nodes, you can’t write independent KCL equations at each node because the current through that source is unknown. The standard approach is to enclose both nodes with a single supernode and write KCL for that entire supernode, summing currents leaving through all elements connected to either node while excluding the current through the voltage source itself. Then you add a constraint equation that expresses the fixed voltage difference imposed by the source between the two nodes. This constraint links the two node voltages, so together with the supernode KCL you obtain solvable equations for the node voltages. If the voltage source were connected to the reference node, you could simply set the corresponding node voltage to the source value and proceed without a supernode. The other options fail because they either ignore the voltage source’s presence, treat only one node, or omit the necessary voltage-relationship constraint, leaving the system underdetermined.