Parallel networks — if you add more resistors in parallel, do total resistance and total current behave as stated? Claim: Adding resistors in parallel increases total resistance and decreases total current.

Introduction / Context:This statement probes the hallmark property of parallel circuits: how total or equivalent resistance changes as additional branches are added, and how that affects the current drawn from a fixed-voltage source.

Given Data / Assumptions:

• Resistors connected in parallel between the same two nodes of an ideal voltage source.
• Ohm’s law applies; source voltage remains constant.
• No wire resistance or parasitic effects.

Concept / Approach:The equivalent resistance of resistors in parallel is found from conductances: 1/Req = 1/R1 + 1/R2 + … . Adding another parallel branch adds positive conductance, so Req must decrease. With a fixed source voltage, the total current Itot = V / Req therefore increases when Req decreases. Thus the claim in the stem is the opposite of the true behavior.

Step-by-Step Solution:

Verification / Alternative check:Numerical example: V = 12 V; R1 = 12 Ω gives Itot = 1 A. Add R2 = 12 Ω in parallel: Req = 6 Ω, Itot = 2 A. Add R3 = 12 Ω: Req = 4 Ω, Itot = 3 A. The pattern confirms the rule.

Why Other Options Are Wrong:

• Choosing “True” confuses parallel with series behavior. Series connections increase resistance as more resistors are added; parallel decreases it.

Common Pitfalls:Using arithmetic averages or adding magnitudes directly; always combine parallel resistances via reciprocals or conductances.

Final Answer:False