---
title: "Parallel Resistors — AP Physics 2 Definition & Exam Guide"
description: "Parallel resistors share the same voltage while current splits among them, making equivalent resistance smaller. Essential for AP Physics 2 compound DC circuits."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/parallel-resistors"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 11"
---

# Parallel Resistors — AP Physics 2 Definition & Exam Guide

## Definition

Parallel resistors are resistors connected across the same two nodes, so each one has the same potential difference while the total current divides among them inversely with resistance; their equivalent resistance (1/Req = 1/R1 + 1/R2 + ...) is always smaller than the smallest individual resistor.

## What It Is

Parallel resistors are [resistors](/ap-physics-2-revised/key-terms/resistor "fv-autolink") wired between the same two junctions in a [circuit](/ap-physics-2-revised/unit-11/2-simple-circuits/study-guide/LROjr9EJ6hjfPDMC "fv-autolink"). Because both ends of every resistor connect to the same two points, each resistor sees the exact same potential difference. The current, on the other hand, splits at the junction. More current flows through the smaller resistance, less through the larger one, in exact inverse proportion (this is the current divider behavior).

The equivalent resistance follows the reciprocal rule, 1/Req = 1/R1 + 1/R2 + ..., which means Req is always **less than the smallest resistor in the group**. Here's the intuition that makes it click: adding a resistor in parallel is like opening another lane on a highway. You haven't made any lane faster, but you've given [charge](/ap-physics-2-revised/unit-10/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1 "fv-autolink") more paths, so more total current flows for the same voltage. More current at the same voltage means lower resistance, by Ohm's law.

## Why It Matters

Parallel resistors live in **[Topic 11.5](/ap-physics-2-revised/unit-11/5-compound-direct-current-dc-circuits/study-guide/FHwqGLM27UrWSc6A "fv-autolink"), Compound Direct Current (DC) Circuits**, where you analyze circuits that mix series and parallel combinations. Almost every compound circuit problem starts by collapsing parallel groups into a single equivalent resistor so you can find the total current from the battery, then working backward to find individual currents and voltages. The parallel rules (same [voltage](/ap-physics-2-revised/key-terms/voltage "fv-autolink"), current divides, reciprocal addition) are also where Kirchhoff's junction rule shows up in concrete form, since the currents splitting into parallel branches must add back up to the total. If you can't handle parallel combinations cleanly, compound circuits, internal resistance problems, and RC circuits all get much harder.

## Connections

### [Series resistors (Unit 11)](/ap-physics-2-revised/key-terms/series-resistors)

Series and parallel are mirror images of each other. In series, resistors share the same [current](/ap-physics-2-revised/unit-11/1-electric-current/study-guide/QaFR8etPqRmh5pdg "fv-autolink") and voltages add; in parallel, resistors share the same voltage and currents add. If you ever forget which rule goes with which, ask what the resistors share. Same path means same current (series), same two nodes means same voltage (parallel).

### Kirchhoff's junction rule (Unit 11)

The current divider behavior of parallel resistors is just the [junction](/ap-physics-2-revised/unit-11/7-kirchhoffs-junction-rule/study-guide/MhZEtEmvXABB5nTQ "fv-autolink") rule in action. Charge is conserved, so the current entering the split must equal the sum of branch currents. The branch with less resistance takes a bigger share, but the total never changes.

### Internal resistance and emf (Unit 11)

Real batteries have [internal resistance](/ap-physics-2-revised/key-terms/internal-resistance "fv-autolink") in series with everything else. A classic compound-circuit setup puts a parallel pair after a battery's internal resistance and wire resistance, then asks how much of the emf is 'lost' before reaching the parallel section. You have to collapse the parallel pair first, then treat the whole circuit as one series loop.

### [Voltage divider (Unit 11)](/ap-physics-2-revised/key-terms/voltage-divider)

The voltage divider is the series-circuit counterpart to the parallel current divider. In series, voltage splits in proportion to resistance; in parallel, current splits in inverse proportion to resistance. Knowing both lets you predict circuit behavior without grinding through full calculations.

## On the AP Exam

Multiple-choice questions love two moves. First, ranking or minimizing equivalent resistance, like asking which arrangement of five identical resistors gives the smallest Req (answer: all five in parallel, giving R/5). Second, conceptual checks on what parallel resistors share, where the answer is always that voltage is the same across every branch. Compound circuit problems push further. A typical setup is a 12.0 V battery with 0.40 Ω internal resistance feeding a 6.0 Ω and 3.0 Ω parallel pair through wires with resistance, and you're asked what fraction of the emf is lost to the internal and wire resistance. The workflow is always the same. Collapse the parallel pair (here, 2.0 Ω), find the total current, then use V = IR on each piece. No released FRQ has used 'parallel resistors' as a standalone term, but circuit-analysis FRQs routinely require reducing parallel combinations as step one, and the justification points often hinge on stating that parallel branches share the same potential difference.

## parallel resistors vs Series resistors

Series resistors carry the same current and their resistances simply add (Req = R1 + R2 + ...), so adding more resistance in series always increases Req. Parallel resistors share the same voltage, current divides among them, and resistances combine by reciprocals, so adding more resistors in parallel always decreases Req. The fastest check on a diagram: if there's only one path through both resistors, they're in series; if the circuit branches and rejoins, they're in parallel.

## Key Takeaways

- Every resistor in a parallel combination has the same potential difference across it, because all of them connect to the same two nodes.
- Current divides among parallel branches in inverse proportion to resistance, so the smaller resistor carries the larger current.
- Equivalent resistance for parallel resistors follows 1/Req = 1/R1 + 1/R2 + ..., and the result is always smaller than the smallest individual resistor.
- For n identical resistors of resistance R in parallel, the equivalent resistance is R/n, which is the smallest Req you can build from those resistors.
- In compound circuits, collapse parallel sections into a single equivalent resistor first, find the total current, then work backward to get individual branch currents and voltages.
- The currents through parallel branches must add up to the total current entering the junction, which is Kirchhoff's junction rule.

## FAQs

### What are parallel resistors in AP Physics 2?

Parallel resistors are resistors connected between the same two junctions, so they all have the same voltage across them while the current splits among the branches. Their equivalent resistance comes from 1/Req = 1/R1 + 1/R2 + ..., and it's tested in Topic 11.5, Compound DC Circuits.

### Does adding more resistors in parallel increase the total resistance?

No, it's the opposite. Every parallel resistor you add opens another path for current, so total current goes up and equivalent resistance goes down. Five identical resistors R in parallel give Req = R/5, the smallest possible Req for that set.

### How are parallel resistors different from series resistors?

Series resistors share one current and their resistances add directly, while parallel resistors share one voltage and combine by reciprocals. The diagram test: one continuous path means series, a branch-and-rejoin means parallel.

### Is the voltage the same across all resistors in parallel?

Yes. Because each resistor connects to the same two nodes, every parallel branch has identical potential difference across it. This is one of the most common conceptual MCQ answers in Unit 11.

### Which resistor in parallel gets more current?

The smaller resistance carries more current, since I = V/R and V is the same for every branch. A 3.0 Ω resistor in parallel with a 6.0 Ω resistor carries exactly twice the current of the 6.0 Ω one.

## Related Study Guides

- [11.5 Compound Direct Current (DC) Circuits](/ap-physics-2-revised/unit-11/5-compound-direct-current-dc-circuits/study-guide/FHwqGLM27UrWSc6A)

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