A series RC circuit contains a capacitor with a reactance of 70 Ω and a resistance of 90 Ω. The applied voltage is 240 V. What are the real, reactive, and apparent power values? What is the power factor? What is the phase angle?

Question

A series RC circuit contains a capacitor with a reactance of 70 [latex]\Omega [/latex] and a resistance of 90 [latex]\Omega [/latex]. The applied voltage is 240 V. What are the real, reactive, and apparent power values? What is the power factor? What is the phase angle?

Accepted Answer

[latex]Z=\sqrt{R^2+X^2}=\sqrt{90^2+70^2}=\sqrt{13,000}=114\Omega[/latex]

[latex]I = V/Z = 240/114 = 2.1 A[/latex]

[latex]S = IV = 2.1(240) = 505.2 VA[/latex]

[latex]Q = I^2X = 2.1^2 imes 70 = 308.7 VAR[/latex]

[latex]P = I^2R = 2.1^2 imes 90 = 396.9 W[/latex]

[latex]PF = R/Z = 90/114 = 0.79 or PF = P/S = 0.79[/latex]

[latex]PF = \cos heta = 0.79[/latex]

[latex] heta = \cos^{-1} 0.79 [/latex]= arcos 0.79 = 37.86°

Question 20.5: A series RC circuit contains a capacitor with a reactance of...

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