Power in AC Circuit: Can Power Be Made Arbitrarily Small?

[ResonantW]

In an AC circuit, the average power dissipated is given by $P=VIcos(\phi)$. Does that mean that in a highly inductive, or highly capacitave, circuit where $\phi$ approaches $\pm \pi/2$, the power can be made arbitrarily small? Even if a resistor were present? Does that mean it wouldn't heat up at all?

 

[russ_watters]

As a fraction of apparent power, real power can be small, but adding a capacitor doesn't reduce the actual value of the real power.

 

[NascentOxygen]

In an AC circuit, the average power dissipated is given by $P=VIcos(\phi)$. Does that mean that in a highly inductive, or highly capacitave, circuit where $\phi$ approaches $\pm \pi/2$, the power can be made arbitrarily small? Even if a resistor were present? Does that mean it wouldn't heat up at all?

In a highly inductive element, there is only a very small component of current that is in phase with the voltage (leaving most to be in phase quadrature). But if resistance is added, then ɸ will no longer be close to Pi/2.

If a current I (RMS) passes through a resistance R, the power loss is I²R. ALWAYS.