Temperature And Resistance

• When a 2V supply is connected to a 60W, 240V bulb it draws a current of 25mA, its resistance is

                                              Thus R=U/I = 2/0.025 =80ohms

• When the same bulb is connected to the correct 240V supply it glows white hot and draws a current of 250mA and its resistance is:

                                             R=U/I = 240/0.250 = 9600ohms

• Thus we can see that a larger current has caused the bulb to get very hot and its resistance has increased by 12 times. To take account of the change in resistance with temperature the temperature coefficient of resistance (α) is used. 
• α for a material at 0°C is the change in resistance of a 1Ω sample of that material when the temperature increases from 0°C to 1°C. Matters are complicated furtherer because it is not easy to measure the resistance of a conductor at 0°C hence, a value for α is often quoted for a temperature increase of 20°C to 21°C. 
• Table 2.2 contains the temperature coefficient of some metals.

•  We can see from the above table that when the temperature increases from 20°C to 21°C the resistance of a 1Ω copper resistance will increase to 1.00396Ω. Thus: 

                                                          Rt=Ro(1+αT)
where:
Rt = total conductor resistance at T (Ω)
R0 = resistance of a conductor at 0°C (Ω)
α = temperature coefficient of resistance
T = temperature (°C)
And: Rt=R20(1+αT)
where:
R20 = resistance of a conductor at 20°C (Ω)
If the resistance of a conductor is not known at the temperature for which α is known the following method can be used:
R1 = the conductor resistance at temperature T1
R2 = the conductor resistance at temperature T2
R1=Ro(1+αT1) and R2=Ro(1+αT2)
Dividing: R1/R2 = (Ro(1+αT1))/(Ro(1+αT2)) = (1+αT1)/(1+αT2)

Hence:
                                   R2=(R11+αT2)/(1+αT1)
Therefore the value of R0 has been eliminated from the equation.