The root-mean-square value of an alternating current is equivalent to the steady direct current that would dissipate heat at the same rate as the alternating current in a given resistor.

For a sinusoidal source,
(a) the root mean square value of the current is given by .
(b) the mean or average power < P > absorbed by a resistive load is half the maximum power. =\frac{1}{2}P_o=\frac{1}{2}{I_o}{V_o}=\frac{1}{2}{I_o}^2R =\frac{V_o^2}{2R}" />.

An a.c. transformer is a device for increasing or decreasing an a.c. voltage. It consists of a primary coil of N_{p} turns and voltage V_{p} and secondary coil of N_{s} turns and voltage V_{s} wrapped around an iron core.

For an ideal transformer (assuming no energy is lost), the following equation is obeyed
.

Power loss in the transmission lines is minimized if the power is transmitted at high voltages (i.e. low currents) since where I is the current through the cables and R is the resistance of the cables.

The equation is often mistakenly used to suggest that power lost is high when voltage of transmission is high. In fact, V refers to the potential difference across the cables, which often have but a fraction of the overall resistance through which the current passes.