Question

Two resistances at 0°C with temperature coefficients 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, temperature coefficient is the average.

Answer 1

The Correct Option is D

Step 1: Let resistances at \( 0^\circ C \) be \( R_1 \) and \( R_2 \). 

Step 2: At temperature \( t \):
\( R = R_1(1+\alpha_1 t) + R_2(1+\alpha_2 t) \) 

Step 3: Effective temperature coefficient:
\( \alpha = \dfrac{R_1\alpha_1 + R_2\alpha_2}{R_1 + R_2} \) 

Step 4: For equal resistances \( (R_1 = R_2) \):
\( \alpha = \dfrac{\alpha_1 + \alpha_2}{2} \)