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## Q. 2.19

Consider the following circuit involving a 60Vvoltage source connected to a network of resistors.Find $v_{x}$.

## Verified Solution

Instead of applying KVL and KCL directly, we first reduce the circuit by considering series and parallel connections of resistors.We have
$R_{eq1} = 8 + 16 = 24 Ω$,

$R_{eq2} = [8 + (6 ∥ 12)] ∥ R_{eq1} = 12 ∥ 24 = 8 Ω$,

$R_{eq3} = 24 + R_{eq2} = 24 + 8 = 32 Ω$,

$R_{eq4} = 4 + 32 ∥ R_{eq3} = 20 Ω$.

Then, after finding the main current to be $i_{x}$ = 3A, we trace back the circuit as follows.

Hence, we obtain
$i_{x}=\frac{1}{2} A$
$v_{x} = 16i_{x} = 8 V$.