# Temperature Coefficient of Resistance

As we discussed in the page under title resistance variation with temperature that electrical resistance of every substance changes with change in its temperature.

**Temperature coefficient of resistance**is the measure of change in electrical resistance of any substance per degree of temperature rise.

_{0}at 0

^{o}C and R

_{t}at t

^{o}C respectively.

From the equation of resistance variation with temperature we get
This α_{o} is called **temperature coefficient of resistance** of that substance at 0^{o}C.
From the above equation, it is clear that the change in electrical resistance of any substance due to temperature rise mainly depends upon three factors-

- The value of resistance at initial temperature,
- Rise of temperature and
- the α
_{o}.

_{o}is different for different materials, so effect on resistance at different temperature are different in different materials.

So the temperature coefficient of resistance __at 0 ^{o}C__ of any substance is the reciprocal of the inferred zero resistance temperature of that substance.

So far we have discussed about the materials that resistance increases with increase in temperature, but there are many materials electrical resistance of which decreases with decrease in temperature. Actually in metal if temperature is increased, the random motion of charged particles and inter atomic vibration inside the materials increases which result to more collisions. More collision resist smooth flow of electrons through the metal, hence the resistance of the metal increases with the increase in temperature. So, temperature coefficient of resistance is considered as positive for metal.
But in case of semiconductor or other non-metal, the number of free electrons increases with increase in temperature. Because at higher temperature, due to sufficient heat energy supplied to the crystal, more numbers of covalent bonds are broken and hence more free electrons are created. That means if temperature increases, more number of electrons comes to the conduction bands from valance band by crossing the forbidden energy gap. As the number of free electrons increases, the resistance of this type of non-metallic substance decreases with increase of temperature. Hence **temperature coefficient of resistance** is negative for non-metallic substances and semiconductors.
If there is approximately no change in resistance with temperature, the value of this coefficient is considered as zero. Such as alloys like constantan and manganin have temperature coefficient of resistance nearly zero.
The value of this coefficient is not constant, it depends on the initial temperature on which the increment of resistance is based. When the increment is based on initial temperature of 0^{o}C, the value of this coefficient is α_{o} - which is nothing but the reciprocal of the respective inferred zero resistance temperature of the substance. But at any other temperature, temperature coefficient of electrical resistance is not same as this α_{o}. Actually for any material, the value of this coefficient is maximum at 0^{o}C temperature. Say the value of this coefficient of any material at any t^{o}C is α_{t}, then its value can be determined by the following equation,
The value of this coefficient at a temperature of t_{2}^{o}C in the term of the same at t_{1}^{o}C is given as,

### Review the Concept of Temperature Coefficient of Resistance

The electrical resistance of conductors such as silver, copper, gold, aluminum etc., depends upon collision process of electrons with in material. As the temperature increase, this electron collision process becomes faster, which results in increased resistance with rise in temperature of conductor. The resistance of conductors generally rise with rise in temperature. If a conductor is having R_{1}resistance at t

_{1}

^{o}C and after raising the temperature, its resistance becomes R

_{2}at t

_{2}

^{o}C. This rise in resistance (R

_{2}- R

_{1}) with rise in temperature (t

_{2}- t

_{1}) depends on following things – By combining above effects, Where, α is the

**temperature coefficient of resistance**of material at t

_{1}

^{o}C. From Equation (1) If at a particular temperature, we know the resistance and

**temperature coefficient of resistance**of material, we can find out the resistance of material at other temperatures by using equation (2). The Temperature Coefficient of Resistance of some Materials or Substances The

**temperature coefficient of resistance**of some materials/substances at 20

^{o}C are listed below-

Sl. No. | Material/Substances | Chemical Symbol/Chemical composition | Temperature coefficient of resistance /^{o}C (at 20^{o}C) |

1 | Silver | Ag | 0.0038 |

2 | Copper | Cu | 0.00386 |

3 | Gold | Au | 0.0034 |

4 | Aluminum | Al | 0.00429 |

5 | Tungsten | W | 0.0045 |

6 | Iron | Fe | 0.00651 |

7 | Platinum | Pt | 0.003927 |

8 | Manganin | Cu = 84% + Mn = 12% + Ni = 4% | 0.000002 |

9 | Mercury | Hg | 0.0009 |

10 | Nichrome | Ni = 60% + Cr = 15% + Fe = 25% | 0.0004 |

11 | Constantan | Cu = 55% + Ni = 45% | 0.00003 |

12 | Carbon | C | - 0.0005 |

13 | Germanium | Ge | - 0.05 |

14 | Silicon | Si | - 0.07 |

15 | Brass | Cu = 50 - 65% + Zn = 50 - 35% | 0.0015 |

16 | Nickel | Ni | 0.00641 |

17 | Tin | Sn | 0.0042 |

18 | Zinc | Zn | 0.0037 |

19 | Manganese | Mn | 0.00001 |

20 | Tantalum | Ta | 0.0033 |

_{o}is the temperature coefficient of resistance of material at 0

^{o}C, then from equation (2), the resistance of material at t

^{o}C, Where, R

_{0}is the Resistance of material at 0

^{o}C Similarly, if the temperature coefficient of resistance of material at t

^{o}C is αt, then the resistance of the material at 0

^{o}C, from equation (2) Where, R

_{t}is the Resistance of material at t

^{o}C From equation (3) and (4) Where, α

_{1}and α

_{2}the

**temperature coefficient of resistance**of material at t

_{1}

^{o}C and t

_{2}

^{o}C respectively. Hence, if we know the

**temperature coefficient of resistance**of a material at a particular temperature, we may find out the temperature coefficient of material at any other temperature by using equation (6). The conducting material are having large and positive temperature coefficient of resistance. Therefore, the resistance of conducting material (metals) rise with rise of temperature. The semiconductors and insulating material are having negative temperature coefficient of resistance. Therefore, the resistance of semiconductors and insulators decrease with rise in temperature. Alloys, such as manganin, constantan etc. are having very low and positive

**temperature coefficient of resistance**. Therefore, the resistance of alloys increase with rise in temperature but this rise in resistance is very low (almost negligible) as compare to metals, which makes these alloys suitable for using in measuring instruments.