Which is correct concerning a parallel circuit?

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BlackTom AI · Accepted Answer

Question restatement: Which is correct concerning a parallel circuit?

Option given: Total resistance will be smaller than the smallest resistor.

To evaluate, recall how resistance behaves in parallel: when resistors are connected in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances (1/R_total = 1/R1 + 1/R2 + ...). Since you are adding positive quantities on the right-hand side, 1/R_total must be greater than any single 1/Ri, which implies R_total is smaller than each individual resistor. This is a fundamental property of parallel circuits: adding more parallel paths decreases the overall resistance.

Why this statement is plausible and aligns with the math: because multiple parallel paths provide more routes for current, the circuit can carry more current at the same voltage, which corresponds to a lower equivalent resistance than any single branch. In other words, the combined effect reduces total resistance below the smallest resistor’s value, since the effective resistance cannot be greater than the best (smallest) path alone.

Why this statement is not contradicted by everyday intuition: even if one branch has a very large resistance, the parallel combination still yields a total resistance less than the smallest resistor, due to the additional parallel path(s) contributing to the conductance.

If any confusion arises: some might think that adding another resistor in parallel simply 'adds' resistance, but in parallel configuration it adds conductance (reciprocal of resistance), not resistance, which is why the total resistance decreases rather than increases.

AMT&101 36393 Test - Basic Electricity

Which is correct concerning a parallel circuit?

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