Resistance, Resistivity, and Ohm's Law
| English | Chinese | Pinyin |
|---|---|---|
| resistance | 电阻 | diàn zǔ |
| resistivity | 电阻率 | diàn zǔ lǜ |
| ohms | 欧姆 | ōu mǔ |
Why does a thin wire get hot while a thick one stays cool?
- Push the same current through a thin wire and it heats up fast.
- The thin wire fights the flow more — it has more resistance 电阻.
- Resistance is how hard a component makes it for charge to pass.
- Two ideas run this lesson: Ohm's law and resistivity.
Ohm's law: V = IR
- For many materials, voltage and current are proportional: $V = IR$.
- The constant $R$ is the resistance, in ohms 欧姆 ($\Omega$).
- On an $I$–$V$ graph this is a straight line through the origin.
- Rearranged: more resistance means less current for a given voltage.
Trace the I–V line
Vary the voltage across a resistor and watch the current follow a straight line.
Ohm's law relates voltage, current and resistance as:
$V = IR$ for an ohmic device.
A $9\ \text{V}$ supply drives $3\ \text{A}$ through a resistor. Find $R$ (in Ω).
$R = V/I = 9/3 = 3\ \Omega$.
Resistivity: material and shape
- Resistance depends on the wire's shape and its material: $R = \dfrac{\rho L}{A}$.
- Resistivity 电阻率 $\rho$ is the material's own opposition to flow.
- Longer wire → more resistance; thicker wire (bigger $A$) → less.
- Copper has low $\rho$ (a good conductor); nichrome has high $\rho$ (a heater).
Using $R = \rho L/A$, a longer, thinner wire has:
More length and less area both raise $R = \rho L/A$.
A material's own opposition to current, symbol $\rho$, is its ____.
Resistivity $\rho$ is the material property in $R = \rho L/A$.
Ohmic vs non-ohmic
- Ohmic devices keep a constant $R$ — a straight $I$–$V$ line.
- Non-ohmic devices (a bulb, a diode) bend the line.
- A bulb's filament heats up, so its resistance rises with current.
- Always check whether $R$ is really constant before using $V = IR$ blindly.
A filament bulb is non-ohmic — its resistance rises as it heats up.
A hot filament has higher resistance, so its I–V line curves.
Select all true statements about resistance.
Ohmic V=IR, R=ρL/A, metals rise with temperature. Bulbs and diodes are non-ohmic.
Temperature matters
- In metals, hotter atoms jostle the electrons more.
- So a metal's resistance increases with temperature.
- That is why a bulb's cold resistance is far below its glowing resistance.
- Some materials do the opposite, and a few lose all resistance (superconductors).
A $12\ \text{V}$ battery drives $3\ \text{A}$ through a resistor. Find $R$.
- $R = \dfrac{V}{I} = \dfrac{12}{3} = 4\ \Omega$.
- Double the voltage and (if ohmic) the current doubles too.
Ohm's law $V = IR$ only holds for ohmic devices with constant $R$. A bulb or diode is non-ohmic — its resistance changes, so its $I$–$V$ graph is a curve, not a line. Don't assume a fixed $R$ for those.
Resistance opposes current: Ohm's law $V = IR$ (ohms), a straight $I$–$V$ line for ohmic devices. Resistivity gives $R = \rho L/A$ — longer and thinner means more resistance. In metals, resistance rises with temperature.