Determine the currents and voltages in the balanced load and the magnitude of the line voltages in Figure 21–26.

Question

Accepted Answer

The load currents equal the specified line currents.

[latex]I _{Z a}= I _{L 1}=1.5 \angle 0^{\circ}[/latex] A

[latex]I _{Z b}= I _{L 2}= 1 . 5 \angle 120^{\circ}[/latex] A

[latex]I _{Z c}= I _{L 3}=1.5 \angle-120^{\circ}[/latex] A

The load voltages are

[latex]V _{Z a}= I _{Z a} Z _{a}[/latex]

= [latex]\left(1.5 \angle 0^{\circ} A ight)(50 \Omega-j 20 \Omega)[/latex]

= [latex]\left(1.5 \angle 0^{\circ} A ight)\left(53.9 \angle-21.8^{\circ} \Omega ight)= 8 0 . 9 \angle- 2 1 . 8 ^ { \circ }[/latex]

[latex]V _{Z b}= I _{Z b} Z _{b}[/latex]

= [latex]\left(1.5 \angle 120^{\circ} A ight)\left(53.9 \angle-21.8^{\circ} \Omega ight)= 8 0 . 9 \angle 9 8 . 2 ^ { \circ }[/latex] V

[latex]V _{Z c}= I _{Z c} Z _{c}[/latex]

= [latex]\left(1.5 \angle-120^{\circ} A ight)\left(53.9 \angle-21.8^{\circ} \Omega ight)= 8 0 . 9 \angle- 1 4 2^{\circ} V[/latex]

The magnitude of the line voltages is

[latex]V_{L}=V_{ heta}=\sqrt{3} V_{Z}=\sqrt{3}(80.9 V )=140 V[/latex]

Question 21.6: Determine the currents and voltages in the balanced load and...