Equivalent resistance in parallel networks: is it accurate to say that the total resistance of a parallel circuit is always greater than the largest single resistor value present?

Introduction / Context:Determining equivalent resistance is central to predicting currents and power. In parallel networks, adding a branch creates an additional current path. This question tests the well-known inequality that the equivalent of parallels is less than the smallest branch resistance, not greater than the largest.

Given Data / Assumptions:

• Two or more resistors in parallel.
• Linear ohmic behavior.
• Ideal measurements without instrument loading effects.

Concept / Approach:For resistors R1, R2, ..., Rn in parallel, 1 / R_eq = sum(1 / R_k). Since reciprocals add, R_eq must be less than or equal to the smallest R_k, with equality only in the trivial single-branch case. Therefore it cannot be greater than the largest resistor; the statement is incorrect.

Step-by-Step Solution:

Verification / Alternative check:Check with R1 = 3 ohm and R2 = 6 ohm: R_eq = (3 * 6) / (3 + 6) = 2 ohm, which is less than 3 ohm (the least), and certainly not greater than 6 ohm (the largest).

Why Other Options Are Wrong:Correct: contradicts the reciprocal rule. Only true for equal resistors: still false; two equal resistors in parallel produce half the value, which is less than either.

Common Pitfalls:Applying series logic to parallel networks; forgetting the reciprocal relationship.

Final Answer:Incorrect