11.3 Resistance, Resistivity, and Ohm’s Law

Describe the resistance of an object using physical properties of that object.

• Resistance is a measure of the degree to which an object opposes the movement of electric charge.
• The resistance of a resistor with uniform geometry is proportional to its resistivity and length and is inversely proportional to its cross-sectional area. Relevant equation:
  • i. Resistivity is a fundamental property of a material that depends on its atomic and molecular structure and quantifies how strongly the material opposes the motion of electric charge.
  • ii. The resistivity of a conductor typically increases with temperature.
  • iii. The total resistance of a resistor with uniform geometry, but that is made of a material whose resistivity varies along the length of the resistor, is given by

Describe the electrical characteristics of elements of a circuit.

• Ohm’s law relates current, resistance, and potential difference across a conductive element of a circuit. Relevant equation:
  • i. Materials that obey Ohm’s law have constant resistance for all currents and are called ohmic materials.
  • ii. The resistivity of an ohmic material is constant regardless of temperature.
  • iii. Resistors can also convert electrical energy to thermal energy, which may change the temperature of both the resistor and the resistor’s environment.
  • iv. The resistance of an ohmic circuit element can be determined from the slope of a graph of the current in the element as a function of the potential difference across the element.