How does resistivity of a conductor very with temperature coefficient of resistivity. Draw the graph of variation of resistivity of a conductor with temperature.

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Solution

$R = R_{0} (1 + α Δ T)$
$e \frac{L}{A} = e_{0} \frac{l_{0}}{A_{0}} (1 + α Δ T)$
$e \frac{l_{0} (1 + α Δ T)}{A_{0} (1 + β Δ T)} e_{0} \frac{l_{0}}{A_{0}} (1 + α Δ T)$
$\Rightarrow e = e_{0} (1 + β Δ T) \Rightarrow e = (1 + 2 α Δ T)$

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How does resistivity of a conductor very with temperature coefficient of resistivity. Draw the graph of variation of resistivity of a conductor with temperature.

R=R0(1+αΔT)eLA=e0l0A0(1+αΔT)el0(1+αΔT)A0(1+βΔT)e0l0A0(1+αΔT)⇒e=e0(1+βΔT)⇒e=(1+2αΔT)

$R = R_{0} (1 + α Δ T)$
$e \frac{L}{A} = e_{0} \frac{l_{0}}{A_{0}} (1 + α Δ T)$
$e \frac{l_{0} (1 + α Δ T)}{A_{0} (1 + β Δ T)} e_{0} \frac{l_{0}}{A_{0}} (1 + α Δ T)$
$\Rightarrow e = e_{0} (1 + β Δ T) \Rightarrow e = (1 + 2 α Δ T)$