Resistance and resistivity
Why the kettle element glows
- A kettle's element gets red-hot, but the cable feeding it stays cool.
- The element has a high resistance — it turns electrical energy into heat.
- Resistance controls where the energy goes.
Resistance
- Resistance $R = \dfrac{V}{I}$, in ohms ($\Omega$).
- It depends on the conditions — especially the temperature.
A component has $12\ \text{V}$ across it and $3.0\ \text{A}$ through it. What is its resistance?
$R = \dfrac{V}{I} = \dfrac{12}{3.0} = 4.0\ \Omega$.
Ohm's law
- A conductor obeys Ohm's law when $I \propto V$ (at constant temperature) — so $R$ is constant.
- This is an experimental result, not the definition. $R = \dfrac{V}{I}$ works for any component.
An ohmic conductor at constant temperature has:
Ohm's law: $I \propto V$, so $R = \dfrac{V}{I}$ is constant and the $I$–$V$ graph is a straight line through the origin.
I–V characteristics
- Metal wire (constant temp): straight line — constant $R$.
- Filament lamp: curves over — heating raises $R$.
- Diode: passes current one way only (above ~0.7 V).
Match each component to its $I$–$V$ characteristic.
Constant $R$ → straight line; heating raises $R$ → flattening curve; a diode blocks reverse current.
A filament lamp's resistance rises at higher voltage because:
More current heats the filament; in a metal, more lattice vibration scatters electrons, so $R$ increases.
Resistivity
- $R = \dfrac{\rho L}{A}$ — $\rho$ is the resistivity, a property of the material ($\Omega\cdot\text{m}$).
- Longer wire → more $R$; thicker wire → less $R$.
A wire has resistivity $2.0 \times 10^{-8}\ \Omega\cdot\text{m}$, length $10\ \text{m}$ and area $2.0 \times 10^{-6}\ \text{m}^2$. Find its resistance.
$R = \dfrac{\rho L}{A} = \dfrac{2.0 \times 10^{-8} \times 10}{2.0 \times 10^{-6}} = 0.10\ \Omega$.
Doubling a wire's length doubles its resistance (same material and area).
$R = \dfrac{\rho L}{A}$, so $R \propto L$ — twice the length, twice the resistance.
Light and heat sensors
- An LDR's resistance falls as light gets brighter (megaohms in the dark, hundreds of ohms in light).
- A thermistor (NTC)'s resistance falls as it gets hotter — both are semiconductors.
Select all the true statements.
LDRs and NTC thermistors (semiconductors) drop in resistance with more light/heat. A metal does the opposite — its resistance rises with temperature.
You've got it
- resistance $R = \dfrac{V}{I}$; Ohm's law: $I \propto V$ at constant temperature
- filament lamp curves because heating raises $R$; a diode is one-way
- resistivity $R = \dfrac{\rho L}{A}$; LDR ↓ with light, thermistor ↓ with heat