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## Q. 1.10

Consider the following circuit involving two voltage sources connected to three resistors.Find the value of $i_{x }$ that passes through the 10V source.

## Verified Solution

• KVL(1 → 2 → 3 → 4 → 1):$−20 + v_{y } + 10 + v_{z } = 0 \longrightarrow v_{y } + v_{z }$ = 10V.
We note that $i_{z } = i_{y }, v_{y } = 10i_{y }, and v_{z } = 5i_{z }= 5 i_{y }$, leading to
$10 i_{y } + 5 i_{y } = 10 \longrightarrow i_{y } = i_{z }$ = 2∕3 A.
Furthermore, $v_{w } = 10V and i_{zw } = v_{w }∕5$= 2A. Finally, applying KCL at node 2, we get
• KCL(2):$i_{y } − i_{x } −i_{w } = 0 \longrightarrow i_{x } = i_{y } − i_{w }$= 2∕3 − 2 = −4∕3A.