Parallel circuits — branch opens: In a parallel network, if one branch becomes open (i.e., the component disconnects so no current flows through that branch), does the total circuit resistance decrease or increase? Give the correct statement about the effect on overall equivalent resistance.

Introduction / Context:
In basic electronics, parallel circuits provide multiple paths for current. Understanding how opening or removing a branch affects the overall equivalent resistance is essential for troubleshooting, reliability analysis, and quick mental calculations in exam and lab settings. This item tests the conceptual link between the number of available current paths and the resulting total resistance seen by the source in a parallel network.

Given Data / Assumptions:

• Network type: resistors connected in parallel.
• Event: one branch opens (no current can flow in that branch).
• Ideal conditions: ideal source and components; wiring resistance and parasitics neglected.

Concept / Approach:
For parallel resistors, 1 / R_eq = 1 / R_1 + 1 / R_2 + ... + 1 / R_n. Each conducting branch contributes a positive term to the total conductance. Removing (opening) one branch removes its conductance term, which reduces the total conductance and therefore increases the equivalent resistance. A decrease in available current paths never decreases the equivalent resistance of a parallel group.

Step-by-Step Solution:

Verification / Alternative check:
Consider two equal resistors R in parallel: R_eq = R/2. If one branch opens, you are left with R only, which is larger than R/2. This confirms that opening a branch raises R_eq relative to the previous value.

Why Other Options Are Wrong:

• Correct: Incorrect choice because R_eq actually increases, not decreases.
• Only true when the source is AC: Source type does not change the parallel resistance identity.
• True only if the remaining branches are identical: Identity of remaining branches does not reverse the rule.
• Cannot be determined: It can be determined from the parallel formula alone.

Common Pitfalls:
Confusing series and parallel behavior; assuming fewer components always means less resistance; forgetting that parallel adds conductances, not resistances. Losing one path removes conductance and increases R_eq.

Final Answer:
Incorrect