Electrical Resistance

The electrical resistance of a wire or circuit is its resistance to the flow of an electrical current. An object made of a good electrical conductor, such as a copper, will have low resistance compared to an identical object made of a poor conductor. Good insulators, such as rubber or glass insulators, have a high resistance. Resistance is measured in ohms (Ω) and is related to the current in the circuit and voltage across the circuit by Ohm’s law, V=IR (where V is voltage, I is current, and R is resistance, all in appropriate units). Resistance is sometimes desirable, as in the electronic components called resistors, which are designed to have a certain amount of resistance. Resistance is, on the other hand, sometimes undesirable, as in wires meant to conduct signals or power from one point to another.

When current flows through an object with nonzero resistance, energy is dissipated as heat. The amount of power (energy per unit time) P dissipated by a resistance R carrying a current I is given by P = I ² R. The power is dissipated in the form of heat. Power loss through resistive heating is why long-distance power lines are designed to have the lowest resistance possible and to operate at high voltage possible; by Ohm’s law, high voltage means low current, and by the power-current law, low current means low power dissipation.

The resistance of a given piece of wire depends of three factors: the length of the wire, the cross-sectional area of the wire, and the resistivity of the material composing the wire. To understand how this works, think of water flowing through a hose. The amount of water flowing through the hose is analogous to the current in the wire. Just as more water can pass through a fat fire hose than a skinny garden hose, a fat wire can carry more current than a skinny wire. For a wire, the larger the cross-sectional area, the lower the resistance; the smaller the cross-sectional area, the higher the resistance. Now consider the length. It is harder for water to flow through a very long hose simply because it has to travel farther. Analogously, it is harder for current to travel through a longer wire. A longer wire will have a greater resistance. The resistivity is a property of the material in the wire that depends on the chemical composition of the material but not on the amount of material or the shape (length, cross-sectional area) of the material. Copper has a low resistivity, but the resistance of a given copper wire depends on the length and area of that wire. Replacing a copper wire with a wire of the same length and area but a higher resistivity will produce a higher resistance. In the hose analogy, it is like filling the hose with sand. Less water will flow through the hose filled with sand than through an identical unobstructed hose. The sand in effect has a higher resistivity to water flow. The total resistance of a wire is then the resistivity of the material composing the wire times the length of the wire, divided by the cross-sectional area of the wire.