Discussion
A network has 10 nodes and 17 branches. The number of different node pair voltages would be :
Answer: C
The number of node pair voltages is 45.
A node pair voltage is the voltage between any two nodes, so the count is the number of ways of choosing 2 nodes out of 10:
\[ \binom{10}{2} = \frac{10 \times 9}{2} = 45 \]
The number of branches does not enter this count. It matters for other quantities: the number of independent loops is b - n + 1 = 17 - 10 + 1 = 8, and the number of independent node voltages is n - 1 = 9. Seven is b - n, 17 is the branch count, and 50 does not follow from either figure.
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