Two conductors have the same resistance at 0 but their temperature coefficients of resistance are α₁ and α₂. The respective temperature coefficients of their series and parallel combinations are nearly (a) (α₁+α₂)/(2), α₁ + α₂ (b) α₁ + α₂, (α₁+α₂)/(2) (c) α₁ + α₂, (α₁α₂)/(α₁+α₂) (d) (α₁+α₂)/(2), (α₁+α₂)/(2)

Answer: (d). Series: Rs = 2R₀(1+(α₁+α₂)/(2)t) ⇒ αs = (α₁+α₂)/(2). Parallel (small α t): Rp ≈ R₀/2(1+(α₁+α₂)/(2)t) ⇒ αp = (α₁+α₂)/(2). The answer is (d).

Two conductors have the same resistance at 0 but their temperature… | JEE Main 2010 (AIEEE)

Q60JEE Main 2010 · AIEEEMedium

Ohm's Law, Resistivity & Temperature

Two conductors have the same resistance at $0^\circ\text{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2.$ The respective temperature coefficients of their series and parallel combinations are nearly

Show answer and solution

Answer: (d)

Series: $R_s = 2R_0\left(1+\tfrac{\alpha_1+\alpha_2}{2}t\right) \Rightarrow \alpha_s = \tfrac{\alpha_1+\alpha_2}{2}$ .
Parallel (small $\alpha t$ ): $R_p \approx \tfrac{R_0}{2}\left(1+\tfrac{\alpha_1+\alpha_2}{2}t\right) \Rightarrow \alpha_p = \tfrac{\alpha_1+\alpha_2}{2}$ .
The answer is (d).

Report a mistake

Ohm's Law, Resistivity & Temperature question from JEE Main 2010 (AIEEE)

More questions on Ohm's Law, Resistivity & Temperature