Determine the value of each current in Figure 15-46, and describe the phase relationship of each with the applied voltage. Draw the current phasor diagram.

Question

Accepted Answer

The resistor current, the capacitor current, and the total current are expressed as follows:

[latex]I_{R}= \frac{V_{s}}{R}= \frac{12\angle 0°V}{220 \angle 0°\Omega } = 54.5 \angle 0° mA[/latex]

[latex]I_{C}= \frac{V_{s}}{X_{C}}= \frac{12\angle 0°V}{150 \angle -90°\Omega } = 80 \angle 90° mA[/latex]

[latex]I_{tot}[/latex]= [latex]I_{R}[/latex]+ j[latex]I_{C}[/latex] = 54.5 mA + j80 mA

Converting [latex]I_{tot}[/latex] to polar form yields

[latex]I_{tot}= \sqrt{I^{2}_{R}+ I^{2}_{C}} \angle an ^{-1} \left(\frac{I_{C}}{I_{R}} ight) [/latex]

[latex]\ \ \ \ \ = \sqrt{(54.5 \ mA)^{2}+ (80 \ mA)^{2}} \angle an ^{-1} \left(\frac{80 \ mA}{54.5 \ mA} ight)= 96.8 \angle 55.7° mA[/latex]

As the results show, the resistor current is 54.5 mA and is in phase with the voltage.The capacitor current is 80 mA and leads the voltage by 90° . The total current is 96.8 mA and leads the voltage by 55.7° . The phasor diagram in Figure 15-47 illustrates these relationships.

Question 15.19: Determine the value of each current in Figure 15-46, and des...

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