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(C) For two resistors in series,the total resistance at temperature $t$ is given by $R_t = R_{1t} + R_{2t}$.Given $R_{1t} = R_1(1 + \alpha_1 t)$ and $

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

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(C) For two resistors in series,the total resistance at temperature $t$ is given by $R_t = R_{1t} + R_{2t}$.Given $R_{1t} = R_1(1 + \alpha_1 t)$ and $R_{2t} = R_2(1 + \alpha_2 t)$.Substituting these into the total resistance equation:$R_t = R_1(1 + \alpha_1 t) + R_2(1 + \alpha_2 t)$$R_t = (R_1 + R_2) + (R_1 \alpha_1 + R_2 \alpha_2)t$$R_t = (R_1 + R_2) \left[ 1 + \frac{R_1 \alpha_1 + R_2 \alpha_2}{R_1 + R_2} t \right]$Comparing this with the standard form $R_t = R_{total}(1 + \alpha_{eff} t)$,where $R_{total} = R_1 + R_2$,we get:$\alpha_{eff} = \frac{R_1 \alpha_1 + R_2 \alpha_2}{R_1 + R_2}$.

Two wires with temperature coefficients of resistance $\alpha_1$ and $\alpha_2$ have resistances $R_1$ and $R_2$ at $0^{\circ}C$. If they are connected in series,what is the effective temperature coefficient of resistance?

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