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(C) When two resistors are connected in series,the equivalent resistance is $R_{eq} = R_1 + R_2$.The change in resistance for a temperature change $\D

Vedclass · Accepted Answer

$\frac{\alpha_1 R_1 + \alpha_2 R_2}{R_1 + R_2}$

Vedclass · Answer

(C) When two resistors are connected in series,the equivalent resistance is $R_{eq} = R_1 + R_2$.The change in resistance for a temperature change $\Delta T$ is given by $\Delta R = R \alpha \Delta T$.For the series combination,the total change in resistance is the sum of the individual changes:$\Delta R_{eq} = \Delta R_1 + \Delta R_2$Substituting the expression $\Delta R = R \alpha \Delta T$ into the equation:$R_{eq} \alpha_{eq} \Delta T = R_1 \alpha_1 \Delta T + R_2 \alpha_2 \Delta T$Since $R_{eq} = R_1 + R_2$,we have:$(R_1 + R_2) \alpha_{eq} \Delta T = (R_1 \alpha_1 + R_2 \alpha_2) \Delta T$Canceling $\Delta T$ from both sides:$\alpha_{eq} = \frac{R_1 \alpha_1 + R_2 \alpha_2}{R_1 + R_2}$

Two wires of resistances $R_1$ and $R_2$ have temperature coefficients of resistance $\alpha_1$ and $\alpha_2$ respectively. If these are joined in series,the effective temperature coefficient of resistance is:

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