The Ohm’s Law Triangle puts voltage above current and resistance so you can quickly choose between (V = IR), (I = V/R), and (R = V/I). For a hypothetical constant-resistance load with 120 V across 10 Ω, the calculated current is 12 A. Use the triangle for an ohmic component or resistive circuit with known operating conditions—not as a shortcut for every electrical load.
Ohm’s Law Formula and Input Table
| Find | Required inputs | Formula | Hypothetical example | Conditions to check |
|---|---|---|---|---|
| Voltage, (V), in volts (V) | Current in amperes (A); resistance in ohms (Ω) | (V = I \times R) | (12\text{ A} \times 10\text{ Ω} = 120\text{ V}) | Current must flow through the resistance being evaluated. |
| Current, (I), in amperes (A) | Voltage in volts (V); resistance in ohms (Ω) | (I = V/R) | (120\text{ V}/10\text{ Ω} = 12\text{ A}) | Voltage must be across that resistance; (R) must be greater than zero. |
| Resistance, (R), in ohms (Ω) | Voltage in volts (V); current in amperes (A) | (R = V/I) | (120\text{ V}/12\text{ A} = 10\text{ Ω}) | Voltage and current must describe the same component and operating condition; (I) must be nonzero. |
These are three rearrangements of the same relationship, not three separate electrical laws. The units also provide a check: one ohm equals one volt per ampere.
The Ohm’s Law Triangle in One Picture
/\
/ \
/ V \
/------\
/ I | R \
/____|_____\
V = I × R
I = V ÷ R
R = V ÷ I
Voltage (V) sits above the horizontal line; current (I) and resistance (R) sit below it. The line represents division, while the side-by-side lower symbols represent multiplication. This layout makes the triangle a memory aid for choosing the correct equation.
How to Read the Triangle
- Identify the unknown: voltage, current, or resistance.
- Cover that symbol in the picture.
- Read the remaining arrangement. Cover (V) to reveal (I \times R); cover (I) to reveal (V/R); cover (R) to reveal (V/I).
- Write the equation with units before inserting numbers.
Writing the equation matters because the picture cannot catch mismatched inputs. For example, using a source’s full voltage with the resistance of only one component can give the wrong answer when other components share the voltage. In a series resistive circuit, calculate total current using total resistance, then calculate each component’s voltage drop using that current.
What V, I, and R Represent
| Symbol | Quantity | Unit | Meaning in the calculation |
|---|---|---|---|
| (V) | Voltage | Volt (V) | Potential difference across the component or circuit section |
| (I) | Current | Ampere (A) | Current flowing through that component or section |
| (R) | Resistance | Ohm (Ω) | Opposition to current under the stated operating conditions |
The letter (I) is the current variable; A is its unit. Likewise, (R) is the resistance variable, while Ω is the unit. Some references use (E) instead of (V) for voltage, so (E = IR) expresses the same relationship.
For constant resistance, increasing voltage increases current proportionally. At constant voltage, increasing resistance reduces current. That relationship helps you check whether an answer moves in the expected direction before relying on its exact value.
Worked Example: 120 V Across 10 Ω
This is a hypothetical calculation, not a recommended mains-voltage experiment or an equipment rating. Assume a steady DC voltage of 120 V directly across a 10 Ω ohmic load, constant operating resistance, and no additional series resistance included in the model.
Calculate the Current
1. Record the known inputs: (V = 120\text{ V}) and (R = 10\text{ Ω}).
2. Select the current formula: (I = V/R).
3. Substitute the values:
[
I = \frac{120\text{ V}}{10\text{ Ω}} = 12\text{ A}
]
4. Check the answer by reversing the calculation:
[
V = IR = 12\text{ A} \times 10\text{ Ω} = 120\text{ V}
]
The result means the modeled load draws 12 A under those assumptions. It does not establish the correct breaker size, conductor size, or permission to install the load.
Check Power Alongside Current
Current alone does not show how much heat a resistor must dissipate. For this resistive example:
[
P = VI = 120\text{ V} \times 12\text{ A} = 1{,}440\text{ W}
]
The same result follows from (P = I^2R = 12^2 \times 10 = 1{,}440\text{ W}). This is calculated dissipation, not a recommended component rating; actual selection must account for the manufacturer’s operating limits and thermal requirements.
For an arithmetic cross-check, use the site’s Circuit Solver alongside the written calculation. A calculator does not replace the applicable NEC requirements, local authority having jurisdiction (AHJ), manufacturer instructions, or professional assessment of the installation.
Choose the Method That Matches the Circuit
| Circuit or load condition | Appropriate approach | Main limitation |
|---|---|---|
| Steady DC, constant-resistance load | Use (V = IR) directly. | Resistance must represent the operating condition. |
| Purely resistive AC load | Use (V_{\mathrm{RMS}} = I_{\mathrm{RMS}}R). | Do not mix RMS and peak quantities. |
| Sinusoidal AC circuit with inductance or capacitance | Use impedance and phasor analysis: (\underline{V} = \underline{I}Z). | Resistance alone omits reactance and phase relationships. |
| Diode or other nonlinear device | Use the device’s voltage-current characteristics. | A single constant resistance does not predict its behavior across operating points. |
| Load with significant temperature change | Use resistance appropriate to the relevant temperature. | Cold resistance may differ from operating resistance. |
The triangle remains useful for resistive portions of a more complicated circuit, but it does not describe every load as a fixed resistor. ROHM’s manufacturer guidance explains the distinction between resistance and AC impedance, while OpenStax explains why nonlinear devices do not follow a constant-resistance relationship.
Common Mistakes When Using the Triangle
The triangle selects an equation; it does not validate the circuit model. A correct calculation can still produce a misleading answer if the voltage, current, resistance, or operating conditions do not belong together.
- Mixing unit prefixes. Convert (10\text{ kΩ}) to (10{,}000\text{ Ω}) and (250\text{ mA}) to (0.250\text{ A}) before substituting. For example, (12\text{ V}/10{,}000\text{ Ω} = 0.0012\text{ A} = 1.2\text{ mA}).
- Mixing branch and whole-circuit values. Use voltage across a branch with that branch’s resistance, or source voltage with the circuit’s equivalent resistance.
- Treating resistance as permanently fixed. Heating can change resistance and therefore current.
- Applying a DC resistance value to a reactive AC load. The relevant relationship may require impedance rather than resistance alone.
- Treating calculated current as final equipment selection. Keep the arithmetic result separate from installation approval and equipment suitability.
For a foundational check, Fluke’s Ohm’s Law explanation provides the three formula forms. For model limits, ROHM’s circuit-design reference covers temperature effects, nonlinear components, and AC impedance.
Ohm’s Law Calculation Checklist
Use this checklist before carrying a result into a design or troubleshooting decision:
- I identified the exact component, branch, or complete circuit being calculated.
- Voltage and current refer to the same circuit section and operating condition.
- I converted inputs to compatible units.
- I confirmed that a resistance-based model applies.
- I kept RMS and peak AC values separate.
- I wrote the formula, substitution, and result with units.
- I checked the answer using a rearranged equation.
- I considered power dissipation where relevant.
- I kept the calculated result separate from code compliance, equipment ratings, and installation approval.