Solution Found!
Find Vo in the network in Fig. P10.18. 3 3 6 1 24 0 V j2
Chapter 10, Problem 10.18(choose chapter or problem)
Find \(\mathbf{V}_{o}\) in the network in Fig. P10.18.
Questions & Answers
QUESTION:
Find \(\mathbf{V}_{o}\) in the network in Fig. P10.18.
Step 1 of 3
Redraw the circuit by representing the mesh currents.
Apply Kirchhoff’s Voltage Law for loop-2,
\( - 24\angle 0^\circ + \left( {{I_2} + {I_1}} \right)3 + \left( {{I_2} - {I_3}} \right)6 = 0\)
\(9{I_2} = 24\angle 0^\circ - 3{I_1} + 6{I_3}\)
From Figure 1, observe the loop current and we get \({I_1} = 4\angle 0^\circ \;{\rm{A}}\).
Substitute the value in the above equation, and we get,
\(9{I_2} = 24\angle 0^\circ - 3 \times 4\angle 0^\circ \;{\rm{A}} + 6{I_3}\)
\({I_2} = \frac{{4\angle 0^\circ + 2{I_3}}}{3}\)
Therefore, the expression for the current is \({I_2} = \frac{{4\angle 0^\circ + 2{I_3}}}{3}\).