In a parallel circuit, how is the reciprocal of the total resistance related to the reciprocals of the individual resistances?

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Study for the Ontario Power Generation (OPG) Orange 1 Test. Ace your exam with multiple choice questions and detailed explanations. Prepare confidently!

Multiple Choice

In a parallel circuit, how is the reciprocal of the total resistance related to the reciprocals of the individual resistances?

Explanation:
In a parallel circuit, multiple paths for current mean the total conductance adds up. Since conductance is the reciprocal of resistance, the total conductance equals the sum of the individual conductances: G_total = G1 + G2 + ... + Gn. Rewriting in terms of resistance, 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. This is the general relationship for any number of parallel resistors. For only two resistors, you could also write R_total = 1/(1/R1 + 1/R2) or R_total = (R1 R2)/(R1 + R2), but the broad, applicable form for many resistors is the sum of reciprocals.

In a parallel circuit, multiple paths for current mean the total conductance adds up. Since conductance is the reciprocal of resistance, the total conductance equals the sum of the individual conductances: G_total = G1 + G2 + ... + Gn. Rewriting in terms of resistance, 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. This is the general relationship for any number of parallel resistors. For only two resistors, you could also write R_total = 1/(1/R1 + 1/R2) or R_total = (R1 R2)/(R1 + R2), but the broad, applicable form for many resistors is the sum of reciprocals.

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