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Explanation:
Let R be the effective resistance
Since it is a parallel combination Voltage remains constant.
current I is not constant
therefore total current I =I1 +I2+I3.....(1)
I=V/R
therefore
V/R = V/R1 +V /R2 +V/R3. (substitute in (1) )
1/R = 1/R1 +1/R2 + 1/R3
therefore R= R1 ×R2× R3 /R1R2 +R1R3 + R2R3
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