Two conductors have the same resistance at 0^ but their temperature coefficients of resistance are α_1 and α_2 . The respective temperature coefficien - Physics MCQ AIEEE 2026 | ExamTest.live

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Two conductors have the same resistance at 0^{\circ} C but their temperature coefficients of resistance are α_{1} and α_{2} . The respective temperature coefficients of their series and parallel combinations are nearly:

Solution & Step-by-step Explanation

Let R_{0} be the resistance at 0^{\circ} C .Series: R_{s} = R_{1} + R_{2} = R_{0} (1 + α_{1} Δ T) + R_{0} (1 + α_{2} Δ T) = 2 R_{0} (1 + \frac{α _{1} + α _{2}}{2} Δ T) .Thus, α_{s} = \frac{α _{1} + α _{2}}{2} .Parallel: R_{p} = \frac{R _{1} R _{2}}{R _{1} + R _{2}} = \frac{R _{0} ( 1 + α _{1} Δ T ) R _{0} ( 1 + α _{2} Δ T )}{R _{0} ( 1 + α _{1} Δ T ) + R _{0} ( 1 + α _{2} Δ T )} $ R_{p} \approx \frac{R _{0}^{2} [ 1 + ( α _{1} + α _{2} ) Δ T ]}{2 R _{0} [ 1 + \frac{α _{1} + α _{2}}{2} Δ T ]} = \frac{R _{0}}{2} [1 + (α_{1} + α_{2}) Δ T] [1 - \frac{α _{1} + α _{2}}{2} Δ T] $ R_{p} \approx \frac{R _{0}}{2} [1 + \frac{α _{1} + α _{2}}{2} Δ T] Thus, α_{p} = \frac{α _{1} + α _{2}}{2} .

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Two conductors have the same resistance at 0^{\circ} C but their temperature coefficients of resistance are α_{1} and α_{2} . The respective temperature coefficients of their series and parallel combinations are nearly:

\frac{α _{1} + α _{2}}{2}, α_{1} + α_{2}

α_{1} + α_{2}, \frac{α _{1} + α _{2}}{2}

α_{1} + α_{2}, \frac{α _{1} α _{2}}{α _{1} + α _{2}}

\frac{α _{1} + α _{2}}{2}, \frac{α _{1} + α _{2}}{2}

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