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## Q. 1.16

Consider the following circuit involving six components, in addition to a given current along a path Find the value of $v_{s}$.

## Verified Solution

Once again, we process the circuit as follows

Using KVL and KCL, we derive
• KVL(1 → 4 → 2 → 1):$−20 + 3 × 8 + 2i_{x}= 0 \longrightarrow i_{x} = −2A$,
• KCL(2): $8 − i_{x} − i_{y} = 0 \longrightarrow i_{y} = 10A$,
• KVL(1 → 2 → 3 → 1): $−2i_{x} + 2i_{y} −v_{s} = 0 \longrightarrow v_{s} = 24V$.
Interestingly, the solution above does not depend on the 3 Ω resistor, and $v_{s}$ is always 24V if this resistor is not zero (not short-circuited). If this resistor was short-circuited, then the question would be inconsistent.