Resistance, Resistivity, and Ohm's Law
Introduced| English |
|---|
| resistance/rɪˈzɪstəns/ |
| Ohm's law/əʊmz lɔː/ |
| ohm/əʊm/ |
| resistivity/ˌriːzɪˈstɪvəti/ |
Some components let charge through easily — others fight it
- Push the same voltage through a thin wire and a thick one; the thin one lets less current through.
- Every component resists the flow of charge to some degree.
- That opposition is its resistance 电阻, and it sets how much current a voltage produces.
- The rule linking them for many materials is Ohm's law 欧姆定律.
Ohm's law
- Resistance is voltage divided by current: $R = \dfrac{V}{I}$, or rearranged $V = IR$.
- Its unit is the ohm 欧姆 ($\Omega$).
- For an ohmic component (like a metal resistor at constant temperature), $R$ is constant.
- Then voltage and current are proportional — a straight line through the origin.
V–I of components
Compare the straight line of a resistor with the curves of a lamp and a diode.
A resistor carries $0.5\ \text{A}$ from a $6\ \text{V}$ supply. What is its resistance, in $\Omega$?
$R = V/I = 6/0.5 = 12\ \Omega$.
Which expresses Ohm's law?
$V = IR$ — voltage equals current times resistance.
What sets a wire's resistance
- A wire's resistance is $R = \dfrac{\rho L}{A}$.
- Longer wire ($L$) ⇒ more resistance; thicker wire (bigger area $A$) ⇒ less resistance.
- $\rho$ is the resistivity 电阻率, a property of the material (copper is low, nichrome is high).
- So resistance depends on the material and the shape of the conductor.
Making a wire longer (same material and thickness) changes its resistance how?
$R = \rho L / A$: a longer $L$ gives a larger resistance.
The material property in $R = \rho L / A$ is called the ____.
Resistivity $\rho$ is an intrinsic property of the material.
Select all ways to increase a wire's resistance.
$R = \rho L / A$ rises with length, resistivity, and thinness. Thicker wire lowers $R$.
Not everything is ohmic
- A filament lamp heats up as current rises, so its resistance increases — a curved graph.
- A diode lets current flow one way but blocks the other — very non-ohmic.
- For these, $R = V/I$ still defines resistance at each point, but it isn't constant.
- Ohm's law ($V \propto I$) holds only when $R$ stays fixed.
A filament lamp is non-ohmic: its resistance rises as it heats up, so its V–I graph curves.
The heating filament's resistance increases with current, bending the graph.
Ohm's law ($V = IR$ with constant $R$) applies only to ohmic components at steady temperature. A filament lamp and a diode are non-ohmic — their resistance changes, so their $V$–$I$ graphs are not straight lines.
A resistor carries $0.5\ \text{A}$ when connected to a $6\ \text{V}$ supply. Find its resistance.
- $R = \dfrac{V}{I} = \dfrac{6}{0.5} = 12\ \Omega$.
Double the voltage to $12\ \text{V}$ and (if ohmic) the current doubles to $1\ \text{A}$.
Resistance $R = \dfrac{V}{I}$ (in ohms) opposes current; for an ohmic component $V = IR$ is a straight line. A wire's resistance is $R = \dfrac{\rho L}{A}$ — more for a long thin wire. Non-ohmic parts (lamps, diodes) have a changing resistance.