Question

Dimension of temperature Coefficient α is

Answer 1

Hint:The constant α is known as the temperature coefficient of the resistance and it symbolizes the change in resistance as per the temperature changes, a positive temperature Coefficient for material means its resistance increases with increase in temperature and vice versa and negative temperature Coefficient for material means its resistance decreases with increase in temperature.


Complete step by step solution:
As we know that,
The resistance of a material at temperature (T) is given by
$R = {R_{ref}}\left[ {1 + \alpha \left( {T - {T_{ref}}} \right)} \right]$
Where,
R = conductor resistance at temperature “T”
Rref = Conductor resistance at reference temperature Tref
$\alpha $= Temperature coefficient of resistance
T = conductor temperature
Tref = Reference temperature that $\alpha $is specified

Dimensional formula for resistance is given by $\left[ {{M^1}{L^2}{T^{ - 3}}{I^{ - 2}}} \right]$
Dimensional formula for temperature is given by $\left[ {{M^0}{L^0}{T^0}{C^1}} \right]$
So from the above equation, the unit of Temperature Coefficient is per degree Celcius
So it’s dimension will be$\left[ {{C^{ - 1}}} \right]$


Note: For pure metals the temperature Coefficient is a positive number also the resistance increases with increase in temperature Carbon, Silicon and Germanium are some of the elements whose temperature Coefficient is negative which means resistance decreases with increase in temperature there is some metal alloys temperature coefficient of resistance is very much close to zero, which means the resistance hardly changes when the temperature is varied.