Effect of adding more branches — as additional resistors are connected in parallel to an existing network, how does the total (equivalent) resistance of the circuit change?

Introduction / Context:
Understanding how equivalent resistance changes with circuit topology is essential for sizing power supplies and estimating currents. This item examines the well-known behavior of parallel combinations when more branches are added.

Given Data / Assumptions:

• One or more resistors are already in parallel.
• An additional resistor is connected in parallel across the same two nodes.
• Ideal lumped components and wiring.

Concept / Approach:
The reciprocal relation for parallel resistances is 1 / R_eq = 1 / R1 + 1 / R2 + ... Adding another positive term (1 / R_new) to the right-hand side increases the total conductance, which means R_eq (the reciprocal of conductance) must decrease.

Step-by-Step Solution:

Verification / Alternative check:
For two equal resistors R in parallel, R_eq = R / 2; adding a third equal branch makes R_eq = R / 3 — a clear decrease with each added branch.

Why Other Options Are Wrong:

• Increase: Opposite to the conductance sum rule.
• Increase by the value of the resistor being connected: That describes series, not parallel.
• Remain unchanged: Only true if the added branch has infinite resistance (i.e., not actually connected).

Common Pitfalls:
Confusing series (resistances add) with parallel (conductances add); forgetting that any finite added branch lowers R_eq.

Final Answer:
Total resistance decreases when more resistors are added in parallel.