Question

Define Temperature co-efficient of resistance. Derive the
expression for temperature co-efficient of resistance.
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Answer 1

Answer:

The temperature coefficient of resistance is defined as the Change in resistance per unit resistance per degree rise in temperature based upon the resistance of 0∘C

Explanation:

What is the derivation of the formula for finding the "temperature coefficient of resistance"?

Temperature coefficient is not something that is derived,just like we don't derive momentum we define it. Same is the case with temperature coefficient of Resistance.

And Temperature coefficient of Resistance is defined as fractional change in resistivity when temperature is increased by an amount dT.

Mathematically,

a(Temperature coefficient ) =dP/P∗dT

P= Resistivity

a=Temperature coefficient

Now,don't think that by mistake i am using word resistivity instead of Resistance.

Actually temperature coefficient is defined in this way only.

Solving above equation we get P=Po∗ea∗(T−To)

Since resistance us proportional to resistivity

Above expression becomes

R(T)=Ro *e a(T−To)

Since a<<1(generally)

Under the approximation that a(T−To)<<1

above expression becomes (which is true for all practical purposes )

R(T)=Ro * (1+a(T−To))

as ea(T−To)=1+a(T−To)+... {Taylor's series

Answer 2

Answer:

Temperature coefficient of resistance is the measure of change in electrical resistance of any substance per degree of temperature change. Let us take a conductor having a resistance of Ro at 0°C and Rt at t°C respectively. This αo is called temperature coefficient of resistance of that substance at 0°C.