state that the reciprocal of the combined resistance of the number of a resistance connected in parallel is equal to the sum of reciprocal of all of all the individual resistance.
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It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination. Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individuals resistances.
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P.F.A the proof below:
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