Find V1 in Fig. E2.30.Figure E2.30

Calculate the value of voltage \(V_{x}\) in the circuit.

$$ \begin{aligned} V_{x} &=(-I)(8 \mathrm{k} \Omega) \\ &=\left(\frac{-32}{24 \mathrm{k}}\right)(8 \mathrm{k} \Omega) \\ &=\frac{-32}{3} \mathrm{~V} \end{aligned} $$

Now, apply Kirchhoff's voltage law to the right hand side loop in the considered circuit and solve for \(V_{1}\).

$$ \begin{aligned} V_{1} &=18-V_{x}-50+8 \mathrm{k} I \\ &=-32-\left(\frac{-32}{3}\right)+(8 \mathrm{k})\left(\frac{32}{24 \mathrm{k}}\right) \\ &=-32+\frac{32}{3}+\frac{32}{3} \\ &=\frac{-(3)(32)+32+32}{3} \end{aligned} $$

Simplify the expression further.

$$ \begin{aligned} V_{1} &=\frac{-96+64}{3} \\ &=\frac{-32}{3} \mathrm{~V} \end{aligned} $$

Therefore, the value of voltage \(V_{a}\) in the circuit is \(\frac{-32}{3} \mathrm{~V}\).