Effect of an open branch on parallel equivalent resistance: when one resistor in a multi-branch parallel circuit opens, does the overall equivalent resistance increase or decrease compared to the intact condition?

Introduction / Context:Reliability issues such as open-circuit faults occur in real systems. Understanding how the equivalent resistance responds is key for predicting source current and power. The tested statement says the total resistance decreases when a branch opens; we evaluate that claim for resistive parallel networks.

Given Data / Assumptions:

• Two or more resistors in parallel; one branch becomes open (infinite resistance).
• Linear ohmic behavior; constant source voltage assumed.
• No compensating control action.

Concept / Approach:In parallel, 1 / R_eq = sum(1 / R_k). Removing a branch sets its contribution 1 / R_open to zero. The sum of reciprocals becomes smaller, so its reciprocal R_eq becomes larger. Therefore opening a branch increases total resistance, not decreases. Consequently, source current drops.

Step-by-Step Solution:

Verification / Alternative check:Example: three equal 6 ohm branches have R_eq = 2 ohm. If one opens, the remaining two yield R_eq = 3 ohm. Resistance increased.

Why Other Options Are Wrong:Correct: contradicts the derived result. Largest branch qualifier: the effect is independent of which branch opens; losing any path increases R_eq. No change: incorrect because the number of parallel paths influences R_eq.

Common Pitfalls:Confusing voltage and current source behaviors; misreading increase vs decrease in equivalent resistance.

Final Answer:Incorrect