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. .
An a.c. transformer is a device for increasing or decreasing an a.c. voltage. It consists of a primary coil of Np turns and voltage Vp and secondary coil of Ns turns and voltage Vs 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.