9.3 Resistance and resistivity

Resistance is R=V/I at an operating point, measured in ohms. It describes how much potential difference is needed for a given current.

For a non-ohmic device the ratio can change with voltage, current or temperature, so call it operating-point resistance when appropriate.

A component carrying 0.50 A at 4.0 V has resistance 8.0 Ω at that point.

Resistance is not “used up” by a component and is not necessarily constant for every material or device.

Ohm’s law states that current is directly proportional to potential difference for a conductor at constant physical conditions: V=IR.

Check temperature and other conditions before applying it. Rearrange only after identifying which quantity is unknown.

A 10 Ω resistor at 5.0 V carries 0.50 A, provided its temperature remains effectively constant.

V=IR defines resistance at a point, but Ohm’s law requires a straight-line proportional relationship over the tested range.

For an ohmic metal kept at constant temperature, current is proportional to voltage, so the I–V graph is a straight line through the origin.

The gradient of an I–V graph is 1/R, whereas the gradient of a V–I graph is R. State which axes are used.

Doubling voltage on a constant-temperature 4 Ω wire doubles current from 0.5 A to 1.0 A.

A curved I–V graph does not mean the device has no resistance; it means resistance changes with operating point.

Increasing current heats a filament, raising its temperature and increasing resistance because lattice vibrations scatter charge carriers more strongly.

Read the curved I–V characteristic rather than assuming V/I is fixed. Cooling on reduction can make the path history relevant.

At higher voltage a lamp’s current rises less than proportionally, showing a larger operating-point resistance.

The lamp is not non-ohmic because current stops; its resistance changes as temperature changes.

A component obeys Ohm’s law only when its V–I relation is proportional under constant conditions, giving constant resistance.

Test proportionality experimentally and identify variables such as temperature. Use a non-linear model or a local resistance when the graph curves.

A fixed resistor can be approximately ohmic over its rated range, while a filament lamp fails the test as it warms.

“Resistance” existing for a device does not prove that V/I stays constant across all voltages.

The resistance of a uniform conductor is R=ρL/A, where ρ is resistivity, L length and A cross-sectional area.

Use the conductor’s material through ρ, and account for geometry: longer wires resist more; thicker wires resist less.

Doubling a wire’s length doubles R, while doubling its diameter quarters R because area scales with diameter squared.

Resistivity is a material property, not the same as the resistance of one particular wire.

A light-dependent resistor’s resistance decreases as light intensity increases, because illumination creates more mobile charge carriers in its semiconductor material.

Use it as a variable sensor: the circuit output depends on how the LDR is arranged with other resistors and the supply.

In a potential divider, brighter light lowers the LDR resistance and changes the share of supply voltage across the other component.

An LDR responds to light intensity, not simply to elapsed time or temperature; the direction of voltage change depends on circuit placement.

For an NTC thermistor, resistance decreases when temperature increases because carrier availability and scattering conditions change in the semiconductor.

The sensor direction must be combined with circuit topology to predict whether an output voltage rises or falls.

In a divider with the thermistor on top, heating it lowers its resistance and lowers the output across it.

“Thermistor resistance decreases” is not enough to predict a voltage without specifying which voltage is measured and where the thermistor sits.