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Electricity · Physics

Resistance links voltage to current in a material.

Ohm’s law describes how current responds to a potential difference. Resistivity is the material property behind resistance, and power tells you how electrical energy is converted to thermal energy.

This topic

Resistance and Resistivity

Apply Ohm’s law, relate resistance to geometry and resistivity, and interpret temperature dependence and power dissipation.

Law
Ohm’s law
Ohm’s law states that for many materials, current is proportional to applied potential difference. The proportionality constant is resistance.
  • Form: V = IR (for ohmic behavior)
  • Meaning of R as “current response” to voltage
  • Ohmic vs non-ohmic devices (conceptual)
  • Interpreting I–V graphs
Start nano-lesson Check if the device is ohmic first.
Material
Resistivity and conductivity
Resistivity is a material property that quantifies how strongly a material opposes current. Conductivity is its inverse.
  • ρ (resistivity) as a property of the material
  • σ = 1/ρ (conductivity)
  • Resistance depends on geometry: longer and thinner → larger R
  • Current density and field connection (preview)
Start nano-lesson ρ is material; R is geometry + material.
Temperature
Temperature dependence
In many metals, resistance increases with temperature because charge carriers scatter more strongly. In semiconductors, behavior can differ.
  • Metals: R typically increases with temperature
  • Scattering picture (qualitative)
  • Linear approximation over modest ranges (intro)
  • Why materials differ in temperature response
Start nano-lesson Temperature changes scattering, not “charge amount.”
Energy
Power dissipation in resistors
Resistors convert electrical energy into thermal energy. Power tells you the rate of energy conversion in a circuit element.
  • Power definition in circuits: P = IV
  • Equivalent forms using Ohm’s law: P = I²R and P = V²/R
  • Interpreting heating and energy usage
  • Safety intuition: why high current heats wires
Start nano-lesson Power is a rate: watts = joules/second.
Practice
Practice & Exercises
Practice using Ohm’s law, relating R to geometry, and computing power dissipation.
  • I–V interpretation: ohmic vs non-ohmic
  • Compute R from ρ, length, and area (conceptual + numeric)
  • Temperature-change questions (intro)
  • Power computations using P = IV, I²R, and V²/R
  • Exam-style resistance and power sets
Open practice sets Write the relation you know: V = IR.