Parallel circuits — effect of an open branch on total resistance In a circuit containing multiple resistors in parallel, what happens to the overall (equivalent) resistance if one of the parallel resistors opens (becomes an open circuit)?

Introduction / Context:
Understanding how faults affect network behavior is essential for troubleshooting. In parallel resistor networks, an “open” means one branch no longer conducts. Knowing how this changes the equivalent resistance helps predict current changes and diagnose failures.

Given Data / Assumptions:

• Two or more resistors are connected in parallel.
• One resistor becomes open (its resistance effectively becomes infinite).
• Supply voltage remains unchanged.

Concept / Approach:
The equivalent resistance of parallel branches is determined by the sum of branch conductances: 1/Req = 1/R1 + 1/R2 + ... . Removing a branch by opening it eliminates its conductance contribution (1/Rbranch → 0). With fewer conducting paths, the total conductance decreases, so the equivalent resistance increases.

Step-by-Step Solution:
Start with: 1/Req = Σ(1/Ri) over all parallel branches.When a branch opens: its term 1/Ropen = 0 (since Ropen → ∞), reducing Σ(1/Ri).With smaller Σ(1/Ri), the reciprocal Req = 1 / Σ(1/Ri) becomes larger.Therefore, the total (equivalent) resistance increases when any conducting branch opens.

Verification / Alternative check:
Example: two 100 Ω resistors in parallel yield Req = (100*100)/(100+100) = 50 Ω. If one opens, only one 100 Ω path remains, so Req jumps from 50 Ω to 100 Ω, clearly an increase.

Why Other Options Are Wrong:

• It halves: halving happens only under specific numeric changes (e.g., adding identical parallel branches), not when removing one.
• It remains the same: losing a path always changes the conductance sum.
• It decreases: adding branches decreases Req; removing branches increases Req.

Common Pitfalls:

• Confusing series and parallel behavior; in series, opening a component breaks the circuit and current falls to zero, but in parallel, other paths still conduct, albeit with higher overall resistance.

Final Answer:
It increases.