题干

AB和CD是完全相同的两条带有绝缘皮的导线,它们并行地埋设在相距2km的甲、乙两地之间.由于两导线之间某处的绝缘外皮受到损伤,而发生了漏电现象(即相当于两根导线之间在漏电处连接了一个电阻.为了确定漏电处的位置,维修人员做了以下测量:

(1)在甲地将两端电压恒为90V的电源的两极分别接在A、C两端,此时在乙地用内电阻很大的电压表测得B、D两端电压为72V.

(2)在乙地将两端电压恒为100V的电源的两极分别接在B、D两端,此时在甲地用同一型号的电压表测得A、C阳端的电压为50V.

如果AB和CD导线每千米电阻值为2Ω,请你根据以上测量结果计算漏电处距甲地多远?绝缘皮破损处的漏电电阻是多大?

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答案(点此获取答案解析)

解:根据题意画等效电路图,如图答1、图答2所示.

因为已知每1km导线的电阻为2Ω,所以2km导线的电阻为4Ω,设MN为漏电处,漏电电阻为R,AM和CN电阻均为r,则MB和ND电阻均为4Ω﹣r.

依题给条件(1)可列方程:72V=90VR+2

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