# Copper loss

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Copper loss is the term often given to heat produced by electrical currents in the conductors of transformer windings, or other electrical devices. Copper losses are an undesirable transfer of energy, as are core losses, which result from induced currents in adjacent components. The term is applied regardless of whether the windings are made of copper or another conductor, such as aluminium. Hence the term winding loss is often preferred. The term load loss is closely related but not identical, since an unloaded transformer will have some winding loss.

## Calculations

Copper losses result from Joule heating and so are also referred to as "I squared R losses", in reference to Joule's First Law. This states that the energy lost each second, or power, increases as the square of the current through the windings and in proportion to the electrical resistance of the conductors.

$\mbox{Copper Loss} \propto I^2 \cdot R$

where I is the current flowing in the conductor and R the resistance of the conductor. With I in amperes and R in ohms, the calculated power loss is given in watts.

Joule heating has a coefficient of performance of 1.0, meaning that every 1 watt of electrical power is converted to 1 Joule of heat. Therefore, the energy lost due to copper loss is:

$\mbox{Copper Loss} = I^2 \cdot R \cdot t$

where t is the time in seconds the current is maintained.

## Effect of frequency

With high-frequency currents, winding loss is affected by proximity effect and skin effect, and cannot be calculated as simply.

For low-frequency applications, the power lost can be minimized by employing conductors with a large cross-sectional area, made from low-resistivity metals.

## Reducing copper loss

Among other measures, the electrical energy efficiency of a typical industrial induction motor can be improved by reducing the electrical losses in the stator windings (e.g., by increasing the cross-sectional area of the conductor, improving the winding technique, and using materials with higher electrical conductivities, such as copper).