立方體電阻

作者:王一哲
日期:2019/3/21

題目

如下圖所示,每個電阻器的電阻值皆為

r,若電流由A流入、由G流出,請問A之間的等效電阻值為何?

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解答

由於電流

I由A點流入之後,往B、D、E的電流皆為
I/3
,可以推測這三個位置等電位,同理可推C、F、H等電位,因此可以將電路圖化簡為下圖,AG之間的等效電阻值為
RAG=r3+r6+r3=56r


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工程師的作法

下圖是用 12 個 10 kΩ 電阻器焊接成而的,用電表測得的電阻值為 8.30 kΩ,與理論值

56×10 相差約 0.4%。

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tags:Physics