Relationship between complex power and quality factor in AC circuits

in06khattab · Apr 17, 2014

Is this true?

Two lines of text: In a RL circuit, φ is positive and Power is leading, Q is positive. In a RC circuit, φ is negative and Power is lagging, Q is negative.

Or is this true?

Handwritten notes: "Impedance phase angle φz is +ve. Voltage leads current by phase angle φz." Below a divider, highlighted: "Current lags voltage. We call this 'lagging power'."

Ø and Q are from this equation:

Equation for complex power: S with a vector arrow = V_rms I_rms e^(jφ) = V_rms I_rms cos φ + j V_rms I_rms sin φ = P + jQ

gneill · Apr 17, 2014

You can play with a few numbers to confirm or refute the statements. Here's how.

Suppose you assume a source voltage of E = 2V RMS. Set your impedance to a convenient value like Z = 1 + 1j Ω for an RL load, or to Z = 1 - 1j Ω for an RC load.

Now, a very handy formula to know is that the complex power is given by S = EI*, where I* is the complex conjugate of the current I (the sign of the imaginary term is reversed). You can determine the current for your sample values as I = E/Z. Plug in the values and see how the various signs and angles turn out.

in06khattab · Apr 17, 2014

Thanks a lot

Relationship between complex power and quality factor in AC circuits

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