Ohm's law and resistance

Ohm's law: for a metal wire kept at the same temperature, the potential difference across it is directly proportional to the current through it. Double the push, double the current.

V = I R

The constant R is the wire's resistance.

The book's activity: connect a wire, an ammeter and a voltmeter, and use one cell, then two, three, four. Record V and I in a table and plot a graph of V against I. It is a straight line through the origin: Ohm's law. The slope of the line is R.

"Why is there resistance?" As electrons move through a wire, they keep bumping into the wire's own atoms, which slows them down. Resistance is measured in ohms (Ω): 1 Ω = 1 V / 1 A. A rheostat is a resistor you can adjust, to control the current.

Resistance depends on four things:

Putting the first three together: R = ρ l / A

ρ (rho) is the resistivity: a property of the material itself, measured in Ω m. A wire's resistance changes if you stretch it or cut it, but its resistivity doesn't: stretched copper is still copper.

Metals have very low resistivity (about 10⁻⁸ to 10⁻⁶ Ω m); insulators such as glass and rubber have very high resistivity. Alloys have a higher resistivity than the metals they are made of and don't oxidise (burn) easily when hot, so they are used in heating elements, such as nichrome in irons and toasters.

Example from the book: a heater draws 4 A at 60 V, so R = 60/4 = 15 Ω. On 120 V, it draws 120/15 = 8 A.