Topic: Network Theory
Two resistances of values 20Ω and 40Ω made of different materials with temperature coefficients of resistance $3~ppm/^{\circ}C$ and $6~ppm/^{\circ}C$ respectively are connected in series. What is the temperature coefficient of resistance of the net resistance?
- A. $5~ppm/^{\circ}C$
- B. $\sqrt{18}ppm/^{\circ}C$
- C. $9ppm/^{\circ}C$
- D. $4.5~ppm/^{\circ}C$
Answer: A. $5~ppm/^{\circ}C$
Explanation: For resistors in series, the equivalent temperature coefficient is the resistance-weighted average of their individual temperature coefficients. Let $R_{eq} = R_1 + R_2 = 20 + 40 = 60~\Omega$. The net temperature coefficient $\alpha_{eq} = \frac{R_1\alpha_1 + R_2\alpha_2}{R_1 + R_2} = \frac{20(3) + 40(6)}{60} = \frac{60 + 240}{60} = \frac{300}{60} = 5~ppm/^{\circ}C$.