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Chapter 1

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}.

Step-by-Step

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.