Find v_{s}(t) in the circuit of Fig. 9.56 if the current i_{x} through the 1-Ω resistor is 0.5 sin 200t A
Question 9.49: Find vs(t) in the circuit of Fig. 9.56 if the current ix thr...
{Z}_{\mathrm{T}}=2+\mathrm{j} 2 \|(1-\mathrm{j})=2+\frac{(\mathrm{j} 2)(1-\mathrm{j})}{1+\mathrm{j}}=4
\begin{array}{l}{I}_{\mathrm{x}}=\frac{\mathrm{j} 2}{\mathrm{j} 2+1-\mathrm{j}} {I}=\frac{\mathrm{j} 2}{1+\mathrm{j}} {I}, \quad \text { where } {I}_{\mathrm{x}}=0.5 \angle 0^{\circ}=\frac{1}{2} \\\\{I}=\frac{1+\mathrm{j}}{\mathrm{j} 2} {I}_{\mathrm{x}}=\frac{1+\mathrm{j}}{\mathrm{j} 4} \\\\{V}_{\mathrm{s}}={I} {Z}_{\mathrm{T}}=\frac{1+\mathrm{j}}{\mathrm{j} 4}(4)=\frac{1+\mathrm{j}}{\mathrm{j}}=1-\mathrm{j}=1.414 \angle-45^{\circ} \\\\\mathrm{v}_{\mathrm{s}}(\mathrm{t})={{1} . {4} 14 \sin \left({2 0 0 t}-{4 5}^{\circ}\right) \mathrm{V}}\end{array}
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