Two networks A and B are connected by two conductors having a net impedance of Z = 0 + j1 Ω, as shown in Fig. 9.15. The voltages at the terminals of the networks are VA = 120 ∠30° V rms and VB = 120 ∠0° V rms. We wish to determine the average power flow between the networks and identify which is

Question

Two networks A and B are connected by two conductors having a net impedance of Z = 0 + j1 Ω, as shown in Fig. 9.15. The voltages at the terminals of the networks are [latex]V_A = 120 \underline{/30^{\circ}}[/latex] V rms and [latex]V_B = 120 \underline{/0^{\circ}}[/latex] V rms. We wish to determine the average power flow between the networks and identify which is the source and which is the load.

Accepted Answer

As shown in Fig. 9.15,

[latex]\begin{aligned}\mathbf{I} &=\frac{\mathbf{V}_{A}-\mathbf{V}_{B}}{\mathbf{Z}} \\&=\frac{120 \underline{/ 30^{\circ}}-120 \underline{/ 0^{\circ}}}{j 1} \\&=62.12 \underline{/ 15^{\circ}} \mathrm{A} \mathrm{rms}\end{aligned}[/latex]

The power delivered by network A is

[latex]\begin{aligned}P_{A} &=\left|\mathbf{V}_{A} ight||\mathbf{I}| \cos \left( heta_{\mathrm{V}_{A}}- heta_{\mathrm{I}} ight) \\&=(120)(62.12) \cos \left(30^{\circ}-15^{\circ} ight) \\&=7200.4 \mathrm{~W}\end{aligned}[/latex]

The power absorbed by network B is

[latex]\begin{aligned}P_{B} &=\left|\mathbf{V}_{B} ight||\mathbf{I}| \cos \left( heta_{\mathrm{V}_{B}}- heta_{\mathrm{I}} ight) \\&=(120)(62.12) \cos \left(0^{\circ}-15^{\circ} ight) \\&=7200.4 \mathrm{~W}\end{aligned}[/latex]

If the power flow had actually been from network B to network A, the resultant signs on [latex]P_{A}[/latex] and [latex]P_{B}[/latex] would have been negative.

Question 9.12: Two networks A and B are connected by two conductors having ...

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