Electrical Resistance When the same p.d. is applied across different conductors, different currents flow. Some conductors offer more opposition or resistance to the passage of current. Definition The resistance, R, of a conductor is defined as the ratio of the potential difference V across it to the current I flowing through it. This can be expressed mathematically as: or V=IR

The unit of measurement of resistance is the ohm, . When a p.d. of 1 volt drives a current of 1 ampere, the resistance is 1 ohm.

I-V Graphs for different materials Metals and Alloys At a constant temperature they have a constant resistance. A I-V graph will show a straight line through the origin. I is proportional to V. They are called linear or ohmic conductors i.e. they obey Ohm’s law:

The resistance of a metallic conductor does not change with p.d. provided the temperature is constant. Note that the gradient of the line is  I /  V This is 1 / R (from V=IR and so R = V / I) Ohmic conductors will always have a straight line characteristic.

Filament Lamps What does the I-V characteristic look like? or

As the resistance increases, the gradient decreases.

Semi-Conductor Diodes Current passes when the p.d. is applied in one direction, but is almost zero in the opposite direction. A diode has a small resistance in one direction but has a large resistance when the p.d. is reversed. Diodes are non-ohmic conductors. I /  A mA V Note that in Forward Bias, it turns on at about 0.7V. 0.7V

Forward Bias - conv. current + - Remember that in Forward Bias, it turns on at about 0.7V.

3V What is the p.d. across each bulb in these circuits? 0.7V Forward Bias 3V - 0.7V 2.3V Reverse Bias I = 0 Almost 3V

Thermistors A thermistor is a semiconductor. As temperature increases, the resistance drops. That is why the gradient of the curve increases. As you heat a semi-conductor up, the number of charge carriers available for conduction (n) increases. I=nave so if n increases, so does I for a given V.

Resistivity The resistance of a conductor depends upon the material that it is made from and also its dimensions (size). For a given volume, the greater the length and smaller the cross sectional area, then the greater the resistance. It is sometimes useful to discuss the property of a material in general rather than that for a particular specimen. We therefore have a property called the resistivity of a material. This is defined as the resistance of a specimen with unit length and unit cross sectional area. Resistivity is measured in ohm metres (  m).

The reciprocal of resistivity is called the conductivity of the material (  ). Conductivity is measured in siemens per metre (Sm -1 ). Silver has one of the highest conductivities, followed by copper. In overhead electricity cables, aluminium is used rather than a more conductive material because of its price and density.

1. If the resistivity of copper is 1.7 x  m, calculate the resistance of 1cm 3 of copper: a)when in the form of a wire of diameter 0.02cm. b)when in the form of a thin sheet 2.5mm thick, the current passing through the sheet perpendicularly to its faces. (17.22 , x  ) Questions

1. If the resistivity of copper is 1.7 x  m, calculate the resistance of 1cm 3 of copper: a)when in the form of a wire of diameter 0.02cm. b)when in the form of a thin sheet 2.5mm thick, the current passing through the sheet perpendicularly to its faces.(17.22 , x  ) Questions

1. If the resistivity of copper is 1.7 x  m, calculate the resistance of 1cm 3 of copper: a)when in the form of a wire of diameter 0.02cm. b)when in the form of a thin sheet 2.5mm thick, the current passing through the sheet perpendicularly to its faces.(17.22 , x  ) Questions