AP® Physics 2: Algebra-Based · Unit 11 · Topic 11.5
Resistors in Parallel
Resistors in parallel give the charge extra paths to flow through, so the combination resists current less than any single resistor alone. Total resistance drops, and current splits between branches based on their resistances.
Parallel resistors sit side by side, each connected across the same two points, so each one gets the full voltage of the battery. Since every branch is a separate route for charge, adding another branch is like opening another lane on a highway: more charge can get through per second for the same voltage push. More current for the same voltage means less resistance, so the equivalent resistance of a parallel combination is always smaller than the smallest individual resistor. For two resistors, 1/R_eq = 1/R1 + 1/R2, which rearranges to the handy product-over-sum form: R_eq = (R1 x R2)/(R1 + R2).
Current divides among parallel branches according to how easy each path is. The smaller resistor carries more current, because it offers less opposition, and the exact split follows I1 = I_total x R2/(R1+R2) - notice the OTHER resistor appears on top. Voltage, meanwhile, stays the same across every branch, which is the opposite behavior from series resistors, where current is shared equally and voltage divides up.
This is why household wiring uses parallel circuits: each lamp or appliance gets full voltage and runs independently, and adding one more only adds another low-resistance path without starving the others. It connects directly to the next idea, combining series and parallel sections in the same circuit, where you reduce parallel chunks to a single equivalent resistance first, then add that to any series resistors.
Key terms
- Equivalent resistance
- The single resistance that would draw the same total current as the whole parallel combination.
- Current divider
- A parallel arrangement that splits total current among branches in proportion to the other branch's resistance.
- Branch
- One of the separate parallel paths that charge can follow between two shared points.
- Conductance
- The reciprocal of resistance, 1/R, which adds directly for parallel resistors.
Watch it explained
- How it worksHow does adding a parallel branch lower the total resistance instead of raising it?
- Worked exampleFind the equivalent resistance of 6 ohm and 12 ohm resistors wired in parallel.
- Worked exampleFind how the 3.0 A from a battery splits between parallel 10 ohm and 20 ohm branches.
- Common mistakeWhy isn't the equivalent resistance of two parallel resistors the average of the two?
Check yourself
End of topic.