In a parallel circuit, the total resistance is always what in relation to the resistance of the lowest value resistor connected to the circuit?

• A. Greater than
• B. Less than
• C. Equal to
• D. Cannot be determined

Answer: (B)

In parallel circuits, multiple paths for current mean the overall opposition to current, or total resistance, is reduced compared to any single path. This happens because the conductance adds up: the reciprocal of the total resistance equals the sum of the reciprocals of each branch.

Since each branch contributes a positive amount to that sum, the total conductance is greater than the conductance of the smallest resistor, which makes the total resistance smaller than that smallest resistor. In other words, the total resistance in a parallel network is always less than the lowest-valued resistor in the network.

A quick check with two resistors in parallel shows this: R_total = (R1*R2)/(R1+R2). If R1 is the smaller one, R_total ends up less than R1 because adding the second path reduces the overall resistance. This logic extends as you add more parallel branches—the total resistance never rises above the smallest individual resistance.