Short on time? This page is the recap. For explanations, the graphs and the worked examples, use the full study guide.
Recap
- Resistance R measures how strongly an object opposes the movement of charge. R = ΔV/I, unit ohm (1 Ω = 1 V/A).
- Resistivity ρ is a property of the material, set by its atomic structure. Resistance is a property of one object and also depends on its shape.
- For most conductors, resistivity increases with temperature: hotter atoms vibrate more and get in the way of drifting electrons more often.
- Ohmic elements keep the same R at every current, so I ∝ ΔV. In the course model, an ohmic material’s resistivity does not change with temperature.
- A filament bulb is non-ohmic: its R rises as it heats up.
- Resistors convert electrical energy into thermal energy, warming the resistor and its surroundings.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| R = ρL/A | ρ in Ω·m, L in m, A in m² | find R from material and shape |
| A = π(d/2)² | d = diameter in m | get the area of a round wire |
| I = ΔV/R | I in A, ΔV in V, R in Ω | link current, potential difference and resistance |
| slope of I against ΔV = 1/R | A/V | read R from a graph |
| slope of R against L = ρ/A | Ω/m | find resistivity from lab data |
| Change to a wire | Effect on R |
|---|---|
| Length × 2 | × 2 |
| Area × 2 | ÷ 2 |
| Diameter × 2 | ÷ 4 |
| Higher-resistivity material | larger, in proportion to ρ |
Assumptions behind the numbers
- The conductor has uniform cross-section along its length.
- “Resistor” means an ohmic element unless the question says otherwise.
- Temperature is constant unless the question is about heating.
- Connecting wires have negligible resistance.
Mistakes to avoid
- Slope = R on an I–ΔV graph. It is 1/R; steeper means smaller R.
- Diameter used as radius, or forgetting to square it.
- mm² → m² with 10⁻³. The factor is 10⁻⁶.
- “Bigger ΔV, bigger R.” For an ohmic element R stays the same.
- “Thicker wire, more resistance.” Thicker means less.
- Calling a curved graph through the origin “ohmic”. It must be straight.
Quick self-check
- A wire is replaced by one of the same metal with three times the length and twice the diameter. By what factor does R change? (× 3/4)
- A resistor carries 0.30 A with 9.0 V across it. What is its resistance? (30 Ω)
- An I–ΔV line through the origin has a slope of 0.050 A/V. What is R? (20 Ω)
- Why does a lamp filament’s resistance rise as it glows? (Its temperature rises, so the resistivity of the metal rises.)
Next: practice questions.