Elect principles -_resistance
- 1. Resistance The resistance of a conductor is, a. directly proportional to its length. (resistance increases with conductor length) b. inversely proportional to its cross-sectional area. (resistance decreases with conductor area) c. dependent on the material composition. (different materials resist the flow of electrons to a lesser or greater extent, this is called resistivity) Resistance can vary slightly with temperature, for all our calculations we will assume a constant temperature.
- 2. Resistivity The resistivity (rho, ρ) of a conductor is dependent upon the ‘willingness’ of the material to allow the flow of electrons. Resistivity has a positive temperature coefficient, meaning that an increase in temperature increases the resistivity of the material. Material ρ Ω/m at 20°C Silver 1.64 x 10-8 Copper 1.76 x 10-8 Aluminium 2.8 x 10-8 Brass 7.2 x 10-8 Eureka 49 x 10-8 Glass 10 x 1012 Mica 9 x 1013 Resistivity of some common materials at 20°C Conductors Insulators {{
- 3. Resistance of a Conductor The resistance (R) of a material is dependent upon the physical dimensions, the material temperature and its resistivity. Knowing these parameters it is possible to determine the resistance of a given sample. The unit of resistance is the Ohm (omega, Ω). where l is the length of the conductor a is its cross sectional area in m2 ρ is the resistivity of the material. Activity Determine the resistance of three different conducting materials with the following dimensions, l = 1km, a = 2.0mm2 . If the cross sectional area were to double what would you expect to happen to the resistance. If the temperature was to rise what would be the effect on the resistance. R = ρ l ohms a
- 4. Resistance and Ohms Law The German physicist Georg Simon Ohm (1789 – 1854) developed a law which defined the relationship between electric current, voltage and resistance from a series of experiments, representing the beginning of electric circuit analysis. Ohm’s Law The current flowing in a circuit is directly proportional to the applied emf and inversely proportional to the resistance of the circuit. I = V amps R R = V ohms I V =IR volts
- 5. Resistance and Ohms Law Activity 1. A 15 ohm resistance is connected to a 30 volt battery, determine the current flowing through the circuit. 2. An ammeter shows that a current of 4 amps is flowing in a circuit. If the supply voltmeter shows that the supply is set to 100 volts determine the circuit resistance. 3. Determine the voltage required to pass a current of 5 amps through a 100 ohm resistance. It is a good idea to sketch these circuits before starting to calculate the results.
- 6. Power Dissipated in Resistance When an electric current passes through a resistance electrons collide with fixed atoms causing energy to transfer from electron to atom and thus work is done. The rate at which work is done is called power, this work causes the resistance to increase in temperature. The unit of power is the Watt, symbol “W”. The power dissipated in a resistance can be determined using any of the three methods below; P = V2 watts R P =VI watts P =I2 R watts
- 7. Power Dissipated in Resistance Activity 1. Determine the power dissipated in a 15 ohm resistance connected to a 30 volt supply. 2. An ammeter shows that a current of 4 amps is flowing in a circuit. If the supply voltmeter shows that the supply is set to 100 volts determine the power taken from the supply. 3. A current of 3 amps flows through a 10 ohm resistance, determine the power dissipated in the resistance. If the resistance has a temperature coefficient of 0.5°C/watt and the ambient temperature is 20°C determine the final temperature reached. It is a good idea to sketch these circuits before starting to calculate your results.