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The temperature coefficient of resistance of a conductor varies as $α = β θ^{2} + γ θ$ . If $R_{0}$ is resistance at $θ = 0$ and $R$ is resistance at $θ_{0}$ , then

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$R_{0} [β θ_{0}^{2} + γ θ_{0}^{3}]$

$R_{0} [\frac{β θ_{0}^{3}}{3} + γ θ_{0}^{2}]$

$R_{0} [\frac{β θ_{0}^{3}}{3} + \frac{γ θ_{0}^{2}}{2}]$

$R_{0} [β θ_{0}^{3} + γ θ_{0}^{2}]$

answer is B.

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Detailed Solution

$d R = R_{0} α d θ$

$R = R_{0} \int_{0}^{θ_{0}} (β θ^{2} + γ θ) d θ$

$= R_{0} [\frac{β θ_{0}^{3}}{3} + \frac{γ θ_{0}^{2}}{2}]$

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