Question

What do you mean by temperature coefficient of resistance being high or low?

Answer 1

Hint: Temperature coefficient relates the change in resistance with change in temperature of the material. If the temperature coefficient is high, a larger fraction of resistance changes with change in temperature. If the temperature coefficient is low, a smaller fraction of resistance changes with change in temperature.

Complete step by step solution:
Resistance of any conductor is the ability to oppose the flow of current through it. Greater is the value of resistance of any conductor, less is the current that will flow through the conductor at any applied voltage.
Temperature coefficient of resistors defines the change in resistance as a function of temperature. It can also be defined as resistance change per degree Celsius of temperature change. Electrical resistance of every substance changes with change in its temperature. It is the measure of change in electrical resistance of any substance per degree of temperature change.
Mathematically understanding, the fractional change in resistor is directly proportional to the change in temperature. Let us take a conductor having a resistance of R0 at 0oC and Rt at to C respectively.
According to the relation between resistance and temperature, where Ro is the temperature at to and Rt is the resistance at any temperature t, we have
$
  \dfrac{{{R_t}}}{{{R_o}}} = \dfrac{{{t_o} + t}}{{{t_o}}} \\
   \Rightarrow {R_t} = {R_o} + \dfrac{{{R_o}t}}{{{t_o}}} \\
   \Rightarrow {R_t} - {R_o} = \Delta R = \dfrac{{{R_o}t}}{{{t_o}}} \\
   \Rightarrow \Delta R = \alpha {R_o}t \\
    \\
 $
Here, α is the temperature coefficient of resistors.
rom the above equation, it's clear that the change in electric resistance of any substance thanks to temperature mainly depends upon three factors –
1.the value of resistance at initial temperature,
2.the rise of temperature and
3.the temperature coefficient of resistance αo. Thus, the fractional change in resistance is directly proportional to the temperature coefficient.

Note: Actually, in metal if the temperature increases, the random motion of free electrons and interatomic vibration inside the metal increase which end in more collisions. More collisions resist the graceful flow of electrons through the metal, hence the resistance of the metal increases with the increase in temperature. So, we consider the temperature coefficient of resistance as positive for metals.