Resistance and Resistivity

Thermistors

-> As current increases, temperature increases -> V increases less than I so resistance decreases

Resistors in parallel

-> By Kirchoff's First Law: I = I1 + I2 -> If R is the total resistance then V = IR or I = V/R -> Also V = I1 x R1 or I1 = V/R1 and V = I2 x R2 or I2 = V/R2 -> Dividing by V gives I/R = I/R1 + I/R2

IV graphs for ohmic component

-> Graph for I against V for an ohmic component will be a straight line through origin as V = IR, I = (1/R)V so gradient = 1/R

Resistors in series

-> If V is pd across both resistors then V = V1 + V2 -> Current passing through each resistor is the same -> If total resistance is R then V = IR -> Also V1 = IR1 and V2 = IR2 -> Follows that IR = IR1 + IR2 -> Dividing by I gives R = R1 + R2

What does the resistance of a piece of wire at a given temperature depend on?

-> Material of the wire it is made from -> Length of the wire L -> Cross sectional area of the wire A. Can be linked by: R = ρL / A where ρ is the resistivity of the material the wire is made from

LDR (Light Dependent Resistor)

-> Resistance decreases with increasing incident light intensity -> In a heat or light sensor, a thermistor or LDR is used as part of a potential divider. It will give an output voltage that depends on temperature or light intensity

Thermistor (NTC - negative temperature coefficient)

-> Resistance decreases with increasing temperature -> In a heat or light sensor, a thermistor or LDR is used as part of a potential divider. Gives an output voltage that depends on the temperature or light intensity

Semi-conductors

-> Resistivity decreases with temperature unlike other conductors -> As temperature increases, more electrons can escape from their atoms and become conducting electrons -> Although there are more collisions with the vibrating ions, it is heavily outweighed by the greater number of electrons

Explain the difference between an ohmic component and a non-ohmic component

Ohmic component -> Has a resistance R that does not change with current and pd eg. fixed resistor Non-ohmic component -> Has a resistance R that changes as the current and pd change. Obeys Ohm's law. eg. filament bulb

Define resistance

Potential difference across the component divided by the current passing through it R = V/I or V = IR -> Units: Ohms (Ω) -> It follows that 1Ω = 1VA^-1

State Ohm's Law

The electric current through a conductor is proportional to the potential difference across it, as long as the temperature remains constant

Define resistivity

The product of the resistance and the cross-sectional area of a wire divided by its length -> Units are Ωm -> Resistivity is a constant for a particular material but does vary with temperature ρ = RA / L -> To determine the resistivity of a piece of wire experimentally: - measure resistance using ohmmeter or measure current through the wire and pd across the wire - measure length of wire with a metre ruler and diameter of wire using a screw gauge micrometer A = πd^2/4