Derivation of resistors connected in parallel
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V=V1=V2=V3--------(1)
I=I1=I2=I3---------(2)
I=V/R----------(3)
Therefore
Substituting 3 in 2
V/R=V1/R1+V2/R2+V3/R3
V/R=V(1/R1+1/R2+1/R3)
Therefore
1/R=1/R1+1/R2+1/R3
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