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## Q. 1.13

Consider the following circuit involving a voltage source and a current source connected to four different resistors.Find the value of $v_{x}$ , that is, the voltage across the 2 Ω resistor. ## Verified Solution

As in the previous examples, we label the nodes, define the directions of the currents, and define the voltages in accordance with the sign convention.

In order to simplify the solution, we again do not define voltage variables separately and
write all equations in terms of currents.ApplyingKVL andKCL consecutively,we obtain
• KVL(2 → 4 → 2): $4i_{y} − 1i_{w} = 0 \longrightarrow i_{w} = 4i_{y}$,
• KCL(4):$i_{y} + i_{w} − i_{z} = 0\longrightarrow i_{z} = 5i_{y}$,

• KCL(3): $i_{z} − i_{x} − 2 = 0\longrightarrow i_{x} = 5iy − 2$,
• KVL(1 → 2 → 4 → 3 → 1): $2i_{x} + 4i_{y} + 6iz − 20 = 0 \longrightarrow i_{y}$ = 6∕11A.
Finally, we have  $i_{x} = 30∕11 − 2 = 8∕11A and v_{x}$ = 16∕11V. 