# Resistivity and Conductivity

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## Resistance

A component's resistance is a measure of how difficult it is to get a current to flow through it.

Resistance = voltage/current

It is measured in ohms (Ω).

Rearranging equations

V=IR and P=IV, so P=I²R.

An I/V graph shows how resistance varies. It has axis of voltage against current,. The shallower the gradient, the greater the resistane. A curve shows the resistance is changing.

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## Using an ohmic conductor

Ohm's law: Provided the temperature is constant, the current through an ohmic conductor is directly proportional to the potential difference across it.

Factors like temperature or light level will have an effect on resistance, so Ohm's law is only true to ohmic conductors at constant temperature.

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## Conductance

Conductance is how well a material can conduct electricity.

Conductance = current/voltage.

As resistance = voltage/current, and conductance = current/ voltage, conductance must equal 1/resistance and resistance must equal 1/conductance.

Because of this, conductance can be measured in Ω^-1, as well as in siemens, S.

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## Filament lamps and thermistors

Filament lamp

The I/V graph for a filament lamp is curved. It starts steep but gets shallower as the voltage rises. This is because it gets hot due to being a coiled up length of wire. Current flowing through the lamp increases its temperature, and the resistance of a metal increases as the temerature increases.

Thermistor

A thermistor is a resistor with a resistance that depends on its temperature. For example, for a particular thermistor, as the temperature rises its resistance may also rise.

Warming the thermistor gives more electrons enough energy to escape fom their atoms. Therefore there are more charge carriers available, so the resistance is lower.

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## Sensitivity

The sensitivity of any sensor is the change in the output value measured for a given chagne in the input variable.

A thermistor's sensitivity is how much its resistance changes compared to the temperature change - which is the same as the gradient of the resistance-temperature graph.

Sensitivity = change in dependent variable/change in independent variable

Its units depends on the two variables.

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