When asking which circuit has three resistors connected in parallel, the direct answer is a parallel resistive network. In this configuration, all three resistors are connected across the exact same two electrical nodes. They share the same voltage potential but divide the total current based on their individual resistance values. Unlike series circuits where current is constant and voltage drops, a parallel topology ensures that if one branch fails open, the remaining branches continue to operate normally.
The Parallel Topology: Node Labels and Core Math
To understand the physics of this circuit, we must define the topology using node labels. Imagine a standard breadboard or PCB layout:
- Node A (Top Rail / V+): The first lead of Resistor 1 (R1), Resistor 2 (R2), and Resistor 3 (R3) all connect to this single common point.
- Node B (Bottom Rail / GND): The second lead of R1, R2, and R3 all connect to this second common point.
Because both ends of every resistor share Node A and Node B, the voltage across each resistor is identical ($V_{R1} = V_{R2} = V_{R3} = V_{source}$). The total equivalent resistance ($R_{eq}$) is calculated using the reciprocal formula:
$$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $$
Worked Numeric Example:
Let's use three standard E24 series carbon film resistors: R1 = 100Ω, R2 = 220Ω, and R3 = 470Ω. Connected across a 12V DC source:
- $1/R_{eq} = (1/100) + (1/220) + (1/470)$
- $1/R_{eq} = 0.0100 + 0.00454 + 0.00212 = 0.01666$
- $R_{eq} = 1 / 0.01666 = \mathbf{60.02\Omega}$
Notice a fundamental rule of parallel circuits: the total equivalent resistance (60.02Ω) is always lower than the lowest individual resistor in the network (100Ω). For a deeper mathematical breakdown of this principle, refer to the parallel resistor circuits chapter on All About Circuits.
Behavior Table and Failure Mode Contrast
A critical advantage of parallel circuits is fault tolerance. To understand what breaks at the extremes, we must contrast parallel behavior with a series string. In a series circuit, a single open resistor breaks the entire path, killing current flow to all components. In parallel, the branches are independent.
| Event / Component Change | Effect on Total Resistance ($R_{eq}$) | Effect on Total Current ($I_{total}$) | Circuit Status & Failure Mode |
|---|---|---|---|
| Baseline (All nominal) | 60.02Ω | 199.9 mA (at 12V) | Normal operation. |
| R2 Opens (Burns out / broken lead) | Increases to 82.4Ω | Drops to 145.6 mA | R1 and R3 continue operating normally. Total current decreases. |
| R2 Shorts (Solder bridge / internal failure) | Drops to ~0Ω | Spikes to maximum (Short Circuit) | Catastrophic. Node A and B are bridged. Power supply trips OCP or traces burn. |
| R1 Value Increases (e.g., to 150Ω) | Increases to 72.1Ω | Drops to 166.4 mA | Current shifts away from R1 branch toward R2 and R3. |
While an open failure in parallel is generally safe and graceful, a short failure in any single branch creates a dead short across the main power supply nodes. Always ensure your voltage source has overcurrent protection (OCP) or a fast-blow fuse rated just above your expected total current.
Design Walkthrough: Sizing Real Components for a 5V Dummy Load
Why choose a three-resistor parallel topology over the alternative (a single high-wattage resistor or a series string)? The primary reasons are thermal distribution, BOM standardization, and redundancy.
The Scenario: You are designing a dummy load to test the overcurrent protection of a 5V USB power bank. You need a total resistance of roughly 10Ω to draw about 500mA ($I = V/R = 5/10 = 0.5A$). The total power dissipated will be $P = V^2/R = 25/10 = 2.5W$.
The Alternatives:
- Single Resistor: You could use one 10Ω 3W or 5W power resistor. However, large wirewound resistors are physically bulky, expensive, and create a massive localized thermal hotspot on your PCB.
- Series String: Three 3.3Ω resistors in series equals 9.9Ω. But if one fails open, your test circuit dies completely.
The Parallel Solution:
Instead, we use three standard, cheap 30Ω 1W metal film resistors in parallel.
- Resistance: $30\Omega / 3 = \mathbf{10\Omega}$ exactly.
- Power Dissipation per Resistor: Each resistor sees the full 5V. $P = 5^2 / 30 = 25 / 30 = \mathbf{0.833W}$.
- Wattage Rating Check: 0.833W is safely below the 1W maximum rating of each component. Total power handled is 2.5W, distributed evenly across three physical packages, keeping the PCB temperature manageable.
By using parallel 30Ω resistors, you leverage standard E12 values, spread the heat across a wider surface area, and ensure that if one resistor suffers a bad solder joint (open), the remaining two (15Ω total) will still draw ~333mA, keeping the test partially active rather than failing silently.
Step-by-Step Breadboard Testing Procedure
Before applying power to a newly designed parallel network, you must verify the topology and branch behavior. Here is how to breadboard and test the 100Ω / 220Ω / 470Ω circuit mentioned in the first section.
- Component Placement: Insert the 100Ω (Brown-Black-Brown), 220Ω (Red-Red-Brown), and 470Ω (Yellow-Violet-Brown) resistors into the breadboard. Ensure one leg of each resistor is in the top shared power rail (Node A) and the other leg is in the bottom shared ground rail (Node B).
- Cold Resistance Check (Power OFF): Set your digital multimeter (DMM) to the 200Ω resistance range. Place the probes across Node A and Node B. Expected reading: ~60Ω. If you read 100Ω, your 220Ω and 470Ω resistors are not making contact. If you read OL (Open Loop), check your breadboard rail continuity.
- Apply Power and Verify Node Voltage: Connect a 12V DC bench power supply to Node A (Red) and Node B (Black). Switch the DMM to DC Voltage (20V range). Measure across R1, then R2, then R3. Expected reading: All three must read exactly 12.0V (±0.1V). If R2 reads less voltage, you have accidental series resistance (like a bad breadboard contact) in that specific branch.
- Measure Branch Currents: Warning: Never measure current in parallel with the voltage source. Switch your DMM to the 10A or mA current jack. Break the circuit at Node A for R1 (pull the leg out of the rail). Place the red probe on the power supply wire and the black probe on the R1 leg. Expected reading for R1: $I = 12V / 100\Omega = 120mA$. Repeat for R2 (expect ~54.5mA) and R3 (expect ~25.5mA).
- Verify Kirchhoff's Current Law (KCL): Add your three measured branch currents together ($120 + 54.5 + 25.5$). The sum should equal the total current measured at the main power supply output (~200mA).
Frequently Asked Questions
What is the equivalent resistance of three identical resistors in parallel?
When all three resistors share the exact same value ($R$), the math simplifies significantly. The equivalent resistance is simply the value of one resistor divided by the total number of resistors: $R_{eq} = R / 3$. For example, three 300Ω resistors in parallel yield exactly 100Ω. This is a common trick used by engineers to achieve specific non-standard resistance values using cheap, bulk-ordered standard components.
Why use a parallel resistor network instead of a single high-wattage resistor?
Thermal management and supply chain logistics. A single 5W resistor requires a large physical footprint, may need a heatsink, and creates a localized hot spot that can degrade nearby sensitive components (like electrolytic capacitors). Three 2W resistors in parallel dissipate the same total heat but spread it across a larger PCB area, improving convective cooling. Furthermore, if a specific high-wattage value is out of stock, combining standard low-wattage values in parallel keeps production moving. For more on practical resistor selection, see the resistors in parallel guide on Electronics Tutorials.
How does adding a fourth resistor in parallel affect the total current?
Adding a fourth resistor in parallel provides an additional path for electrons to flow. Because $R_{eq}$ decreases when any new parallel branch is added, the total current drawn from the voltage source increases (assuming a stiff voltage supply). However, the current flowing through the original three resistors remains exactly the same, as their branch voltages have not changed.
Can I mix different wattage ratings in a parallel resistor circuit?
Yes, but you must calculate the power dissipation for each branch individually. In a parallel circuit, voltage is constant across all branches. Power is calculated as $P = V^2 / R$. A lower-resistance branch will draw more current and dissipate more heat, regardless of its physical size. Ensure that the calculated $V^2 / R$ for each specific resistor is at least 20% to 50% below its individual maximum wattage rating to prevent thermal runaway and drift.
