A circuit has 5 nodes (including the reference/ground node). How many independent node voltage equations must you write to solve the circuit (assuming no voltage sources)?
A5
B4
C3
DIt depends on the number of branches
The node voltage method requires one equation per non-reference node, which is always (total nodes - 1). With 5 nodes, you write 4 equations. The reference node is assigned v = 0, so it does not need an equation. The number of branches affects how many terms appear in each equation, not how many equations you need.
Question 2 True / False
When a voltage source connects two non-reference nodes, you can write a standard KCL equation at each of those two nodes independently.
TTrue
FFalse
Answer: False
A voltage source between two non-reference nodes creates a supernode. You cannot write individual KCL equations at each node because the current through the voltage source is unknown. Instead, you treat the two nodes as a combined supernode — writing one KCL for the boundary of the supernode as a whole — and add a separate constraint equation from the voltage source: v_a - v_b = V_s.
Question 3 Short Answer
Why is the reference node assigned a voltage of zero, and how does the choice of reference node affect the final answer?
Think about your answer, then reveal below.
Model answer: The reference node is assigned v = 0 by definition to give all other voltages a common baseline to be measured against. The choice of reference does not change the physical voltages across elements or branch currents; it only changes which node voltages are positive or negative. Choosing a node with many connections simplifies the algebra by reducing the number of terms per equation.
Node voltages are potential differences relative to a chosen datum. Any node can serve as ground — the circuit physics are unchanged. Choosing the node with the most connections is a practical convenience: every branch connected to ground contributes a simple v_k/R term rather than (v_k - v_j)/R, reducing algebraic complexity.