Question

Two resistances at 0^∘C with temperature coefficient of resistance alpha₁ and alpha₂ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be:

• A. \(\alpha_1+\alpha_2\)
• B. \(\dfrac{\alpha_1\alpha_2}{\alpha_1+\alpha_2}\)
• C. \(\dfrac{\alpha_1-\alpha_2}{2}\)
• D. (alpha₁+alpha₂)/(2)

Hint:

For series combination of equal resistances: alphaₑq=average of individual α

Answer 1

The Correct Option is D

Step 1: Let the resistances at 0^∘C be equal (R and R). At temperature t: R₁=R(1+alpha₁ t), R₂=R(1+alpha₂ t)
Step 2: Series combination: Rₑq=R₁+R₂ =2R[1+(alpha₁+alpha₂)/(2)t]
Step 3: Hence the effective temperature coefficient is: alphaₑq=(alpha₁+alpha₂)/(2)