Ohm's Law

Ohm’s Law is the single most important formula in electrical work. It describes the relationship between voltage, current, and resistance in any electrical circuit. You will use it every day — when troubleshooting a circuit, sizing conductors, checking loads, or verifying that a circuit is operating within safe limits.

The Formula

$V = I \times R$

Where:

• $V$ = Voltage in volts (V) — the electrical pressure pushing current through the circuit
• $I$ = Current in amperes/amps (A) — the flow of electrons through the conductor
• $R$ = Resistance in ohms ($\Omega$) — the opposition to current flow

Rearranging the Formula

Since Ohm’s Law is a simple linear equation, you can solve for any variable:

$V = I \times R \quad \text{(find voltage)}$

$I = \frac{V}{R} \quad \text{(find current)}$

$R = \frac{V}{I} \quad \text{(find resistance)}$

The Ohm’s Law Triangle

A quick memory aid used on the job: draw a triangle with $V$ on top and $I$ and $R$ on the bottom. Cover the variable you need, and the remaining two show you the formula.

Units at a Glance

Prefixes you will encounter: kilohm ($\text{k}\Omega$ = 1,000 $\Omega$), milliamp (mA = 0.001 A), megohm ($\text{M}\Omega$ = 1,000,000 $\Omega$).

Worked Examples

Example 1: Finding Current in a 120V Circuit

Scenario: You connect a 120V branch circuit to a baseboard heater with a resistance of 12 $\Omega$. What current will flow?

$I = \frac{V}{R} = \frac{120 \text{ V}}{12 \text{ }\Omega} = 10 \text{ A}$

Answer: The circuit draws 10 amps. This is well within the rating of a 20A breaker and #12 AWG copper wire.

Example 2: Finding Voltage Drop Across a Load

Scenario: A motor on a 240V circuit draws 20A. The conductors have a combined resistance of 0.6 $\Omega$ from the panel to the motor. What is the voltage lost in the wire?

$V_{\text{drop}} = I \times R = 20 \text{ A} \times 0.6 \text{ }\Omega = 12 \text{ V}$

Answer: The conductors drop 12 volts. That means the motor actually receives $240 - 12 = 228$ V. The percentage drop is $\frac{12}{240} \times 100 = 5\%$, which is at the NEC recommended maximum for branch circuit plus feeder combined.

Example 3: Finding Resistance of a Heating Element

Scenario: A 240V water heater draws 18.75A at full load. What is the resistance of the heating element?

$R = \frac{V}{I} = \frac{240 \text{ V}}{18.75 \text{ A}} = 12.8 \text{ }\Omega$

Answer: The element resistance is 12.8 ohms. If you measure the element with an ohmmeter and get a significantly different reading, the element may be failing.

Quick Reference: Ohm’s Law Formulas

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Common Mistakes to Avoid

1. Confusing voltage and current. Voltage is the pressure (like water pressure), current is the flow (like gallons per minute). They are related but not the same.
2. Using the wrong voltage. Residential circuits are either 120V or 240V. Commercial systems may be 208V, 277V, or 480V. Always use the actual system voltage, not a guess.
3. Forgetting that wire has resistance. The load is not the only resistance in the circuit. Long conductor runs add resistance that causes voltage drop.
4. Mixing units. If resistance is in kilohms, convert to ohms first. $4.7 \text{ k}\Omega = 4{,}700 \text{ }\Omega$.

Key Takeaways

• Ohm’s Law ($V = I \times R$) relates voltage, current, and resistance in every DC and AC resistive circuit
• You can rearrange it to solve for any one of the three quantities
• Always use correct units: volts, amps, and ohms
• On the job, Ohm’s Law helps you find expected current draw, check voltage drop, and verify element resistance
• This formula is the foundation for power calculations, voltage drop, and wire sizing

Math for Electricians