电阻的并联公式是怎样推导而来的？求详解。 并联电阻计算公式计算方法
\u7535\u963b\u5e76\u8054\u516c\u5f0f\u63a8\u5bfc\u600e\u4e48\u63a8\u5bfc\u5047\u8bbe\u4e09\u4e2a\u7535\u963b\u5e76\u8054
I=I1+I2+I3
U=U1=U2=U3
\u4e0a\u5f0f\u9664\u4ee5\u4e0b\u5f0f\u5f97
I/U=I1/U1+I2/U2+I3/U3
\u53731/R=1/R1+1/R2+1/R3
\u5982\u679c\u662f\u4e24\u4e2a\u7535\u963b\u5e76\u8054
1/R=1/R1+1/R2
=(R1+R2)/R1R2
\u6240\u4ee5R=R1R2/R1+R2
\u603b\u7535\u963b\u503c\u7684\u8ba1\u7b97
1/R\u603b=1/R1+1/R2+\u2026\u2026+1/Rn\uff0c\u5373\u603b\u7535\u963b\u7684\u5012\u6570\u7b49\u4e8e\u5404\u5206\u7535\u963b\u7684\u5012\u6570\u4e4b\u548c
\u7279\u522b\u7684\uff0c\u4e24\u7535\u963b\u5e76\u8054\u603b\u503c\u4e3a\uff1a R\u603b=\uff08R1*R2)/\uff08R1+R2\uff09
\u5bf9\u4e8en\u4e2a\u76f8\u7b49\u7684\u7535\u963b\u5e76\u8054\uff0c\u516c\u5f0f\u5c31\u7b80\u5316\u4e3aR\u5e76=R/n\u3002
\u6bd4\u5982\u95ee\u9898\u4e2d\u4e00\u4e2a\u7535\u963b20\u6b27\uff0c\u53e6\u4e00\u4e2a\u7535\u963b\u662f40\u6b27\uff0c\u5e76\u8054\u5728\u4e00\u8d77\u603b\u7535\u963b\u8ba1\u7b97\u65b9\u6cd5
\u2460\u5229\u7528\u516c\u5f0f R\u603b=\uff08R1*R2)/\uff08R1+R2\uff09
R\u603b=20*40/\uff0820+40\uff09=40/3
\u2461\u6309\u7167\u7535\u963b\u5e76\u8054\u516c\u5f0f 1/R\u603b=1/R1+1/R2+\u2026\u2026+1/Rn\uff0c\u5c06\u6bcf\u4e2a\u5206\u7535\u963b\u7684\u5012\u6570\u76f8\u52a0\uff0c\u518d\u6c42\u548c\u7684\u5012\u6570\u5c31\u662f\u5e76\u8054\u7684\u603b\u7535\u963b \u3002\u53731/20+1/40=3/40 \u90a3\u4e48\u603b\u7535\u963b\u5c31\u662f= 40/3\u3002
\u2460\u2461\u4e24\u79cd\u8ba1\u7b97\u7ed3\u679c\u76f8\u540c\uff0c\u5747\u662f40/3\uff0c\u7ea6\u7b49\u4e8e13.3\u3002
\u6269\u5c55\u8d44\u6599\uff1a1\u3001\u5e76\u8054\u7535\u8def\uff1a\u5e76\u8054\u7684\u5404\u652f\u8def\u7535\u538b\u76f8\u7b49\uff0c\u5e72\u8def\u7535\u6d41\u7b49\u4e8e\u5404\u4e2a\u652f\u8def\u548c\u3002
\u8868\u8fbe\u5f0f\uff1a\u7535\u963bR1R2R3\u2026\u2026Rn\u5e76\u8054,\u7535\u538bU1=U2=\u2026\u2026=Un\u5e72\u8def\u7535\u6d41\uff1aIn=I1+I2+\u2026\u2026+In\u7531\u4e8eP=UI,I=U/R\uff0c\u4ee3\u5165\uff0c\u5e76\u8054\u7535\u963b\u7684\u529f\u7387\u6bd4P1:P2:P3\u2026\u2026\uff1aPn=U1^2/R1:U2^2/R2\u2026\u2026Un^2/Rn=1/R1:R2\u2026\u20261/Rn\u7531\u4e8e\u662f\u7eaf\u7535\u963b\uff0c\u53d1\u70ed\u6bd4Q1:Q2\u2026\u2026\uff1aQn=Pn\u6bd4=1/R1:R2\u2026\u20261/Rn\u3002
2\u3001\u5e76\u8054\u7535\u8def\u4e2d\u7684\u5173\u7cfb
\u7535\u538b\u7684\u5173\u7cfb\uff1aU=U1=U2
\u7535\u6d41\u7684\u5173\u7cfb\uff1aI=I1+I2
\u7535\u963b\u7684\u5173\u7cfb\uff1a1/R=1/R1+1/R2
\u7535\u529f\u7684\u8ba1\u7b97\uff1aW=UIt
\u7535\u529f\u7387\u7684\u5b9a\u4e49\u5f0f\uff1aP=W/t
\u5e38\u7528\u516c\u5f0f\uff1aP=UI
\u7126\u8033\u5b9a\u5f8b\uff1aQ\u653e=I^2Rt
\u5bf9\u4e8e\u7eaf\u7535\u963b\u7535\u8def\u800c\u8a00\uff1aQ\u653e=I^2Rt =U^2t/R=UIt=Pt=UQ=W
\u7167\u660e\u7535\u8def\u7684\u603b\u529f\u7387\u7684\u8ba1\u7b97\uff1aP=P1+P1+\u2026\u2026
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1-\u5e76\u8054\u7535\u963b
而 U＝U1＝U2 ，I＝I1＋I2
所以 I / U＝（I1＋I2）/ U＝（I1 / U）＋（I2 / U ）＝（I1 / U1）＋（I2 / U2 ）
得 1 / R并＝（1 / R1）＋（1 / R2 ）
结论：并联电路的总电阻的倒数等于各个电阻倒数之和。
假设两电阻R1，R2并联，可知两端电压相等，假设为U
则电流
I1=U/R1;I2=U/R2；
流过两电阻的总电流:
I=I1+I2=U/R1+U/R2=U(1/R1+1/R2)=U(R1+R2)/R1*R2;
假设此两电阻的并联等效电阻位R有：
R=U/I=U/(U(R1+R2)/R1*R2)=R1*R2/(R1+R2);
即：R=R1*R2/(R1+R2)得证
欧姆定理
(R1*R2)/(R1+R2)=R并
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