2022年度 電験3種 下期 - 理論 - 問7 2022年度 下期 理論 問7

20℃での並列抵抗：\( r_{20} = \dfrac{R_{1}R_{2}}{R_{1}+R_{2}} \)
21℃（温度上昇 \( \Delta T=1 \)）での抵抗値：
\( R_{A}' = R_{1}(1+\alpha_{1}) \)
\( R_{B}' = R_{2} \)（\( \alpha_{2}=0 \)のため不変）
21℃での並列抵抗：
\[ r_{21} = \dfrac{R_{1}(1+\alpha_{1})R_{2}}{R_{1}(1+\alpha_{1})+R_{2}} = \dfrac{R_{1}R_{2}(1+\alpha_{1})}{R_{1}+R_{2}+\alpha_{1}R_{1}} \]
変化率 \( \dfrac{r_{21}-r_{20}}{r_{20}} = \dfrac{r_{21}}{r_{20}} - 1 \) を計算する。
\[ \dfrac{r_{21}}{r_{20}} = \dfrac{R_{1}R_{2}(1+\alpha_{1})}{R_{1}+R_{2}+\alpha_{1}R_{1}} \times \dfrac{R_{1}+R_{2}}{R_{1}R_{2}} = \dfrac{(1+\alpha_{1})(R_{1}+R_{2})}{R_{1}+R_{2}+\alpha_{1}R_{1}} \]
\[ \dfrac{r_{21}}{r_{20}} - 1 = \dfrac{R_{1}+R_{2} + \alpha_{1}R_{1} + \alpha_{1}R_{2} - (R_{1}+R_{2}+\alpha_{1}R_{1})}{R_{1}+R_{2}+\alpha_{1}R_{1}} = \dfrac{\alpha_{1}R_{2}}{R_{1}+R_{2}+\alpha_{1}R_{1}} \]
よって、(2)が正しい。