Resistance

The electrical resistance of an object is the measure of its opposition to a given current. It can be thought of as similar to friction, but for currents. It is dependent on multiple properties of the object, like the nature of the object itself, its length in the circuit, and its cross-sectional area. Resistance is measured in SI units of ohms(Ω). The formula for the resistance R is:

where rho is the electrical resistivity of the object, given by the nature of the object itself, measured in ohm-meters. For example, iron has an electrical resistivity of 1 * 10^-7 ohm-meters whereas carbon graphite has one of 1 * 10^-5, which makes sense as you'd expect carbon to cause more electrical resistance than iron. The electrical resistivity is the inverse of the object's electrical conductivity so the better an object is at conducting electricity, the worse it is at resisting electricity, which you'd expect:

The electrical conductivity, given by lower case sigma, can be expressed mathematically this way, in units of 1/(ohm-meters).

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In the equation for resistance, L represents the length of the resistor and A represents the cross-sectional area of the resistor.

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If the change in temperature isn't too large, a linear approximation can be used to determine the resistance of an object with respect to its change in temperature. Lower-case alpha is a constant(with units 1/K or 1/C) that defines how easily heating the resistor expands the resistance.