We saw that when a wire is connected to the terminals of a battery with voltage (V), a current (I )will flow through the wire. Experiments show that the current (I ) depends on the physical characteristics of the wire: length, cross-sectional area, and conductivity. Conductivity, or its inverse resistivity, is determined by chemical composition of the wire and its temperature.

Experiments also show that if the temperature of a wire remains constant, the current is directly proportional to the voltage. This is called Ohm's law and it means we can define the resistance of a wire in the following way:

ohm



where L is the length of the wire, ρ is the resistivity of the wire, and A is the area of the wire. The units of resistance are ohms. An ohm is a volt/amp.

  1. Explain why the current a) varies directly with the area of the wire b) varies inversely with the length of the wire c) decreases when the temperature of the wire decreases d) depends on the atomic structure of the wire
  2. Explain why Ohm's law is true. Is it a definition? Is it an experimental fact? Can it be understood in terms of the motion of electrons in the wire?
  3. What current flows between a potential difference of 120 Volts through a resistance of 30 ohms?
  4. A resistance of 30 ohms is placed across a 90-V battery. What current flows in the circuit?
  5. A current of 0.5 A flows through a lamp when it is connected to a 120-V source. What is the resistance of the lamp?