State the average power formula for a sinusoidal AC circuit using rms quantities.

What is the power factor of an AC circuit?

What is the average power dissipated by an ideal inductor or ideal capacitor over a full cycle?

An AC circuit has \(V_{\mathrm{rms}}=120\,\mathrm V\), \(I_{\mathrm{rms}}=2.0\,\mathrm A\), and power factor \(0.80\). Find average power.

A series circuit has \(I_{\mathrm{rms}}=3.0\,\mathrm A\) and \(R=25\,\Omega\). Find average power.

A series circuit has \(R=30\,\Omega\) and \(Z=50\,\Omega\). Find the power factor.

A device draws \(5.0\,\mathrm A\) rms from a \(230\,\mathrm V\) rms supply at power factor \(0.70\). Find its average power and apparent power.

A series LRC circuit has \(V_{\mathrm{rms}}=100\,\mathrm V\), \(R=20\,\Omega\), and \(Z=40\,\Omega\). Find \(I_{\mathrm{rms}}\), power factor, and average power.

Derive \(P_{\mathrm{avg}}=I_{\mathrm{rms}}^2R\) for a series LRC circuit from \(P_{\mathrm{avg}}=V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi\).

The instantaneous voltage and current are \(v=V_0\cos\omega t\) and \(i=I_0\cos(\omega t-\phi)\). Show that the average power is \(V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi\).