Resistance
Consider a battery connected to a light bulb in a circuit. A current flows through the light bulb.
The light bulb is between points B and C. The amount of work needed to move 1 coulomb of charge from B to C is the potential difference, or p.d. The larger the p.d., the larger the current.
For current in a metal wire, the current is usually proportional to the p.d. This means that if p.d. doubles, current also doubles. This in turn means that the ratio of p.d. to current is constant. This ratio is called the resistance. So
resistance = p.d./current, or resistance = voltage/current.
This is often written as
R = V / I,
where V is the voltage, I is current, and R the resistance is a constant. The unit of resistance is Ohms (Ω). The relation between voltage and current is called Ohm's law.
Wikipedia: Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points.
Exercise. The potential difference across a light bulb is 1 V. Current through the bulb is 0.1 A. What is the resistance of the light bulb?
Answer. Using Ohm's law R = V / I, we find R = 1 / 0.1 = 10 Ω.
Exercise. Resistance of a light bulb is 20 Ω. Potential differennce across the bulb is 1 V. What is the current through it?
Answer. Rearrange Ohm's law R = V/I to make I the subject. Multiply by I and divide by R: I = V/R. So current is I = 1/20 = 0.05 A.
Exercise. Resistance of a light bulb is 10 Ω. Current through the bulb is 200 mA. What is the potential difference across the bulb?
Answer. Rearrange Ohm's law R = V/I to make V the subject. Multiply by I: V = IR. The current must be converted to SI unit first: 200 mA = 0.2 A. So the potential difference is V = 0.2 x 10 = 2 V.