Ohms Law

Why Ohm’s Law Matters

In the last lesson you built a simple circuit and identified its source, path, switch, load and return path.

Ohm’s Law gives us a mathematical way to describe what is happening in that circuit.

If you know any two of these three values:

Voltage
Current
Resistance

you can calculate the third.

The Three Values in Ohm’s Law

You will see these symbols repeatedly throughout electrical theory and troubleshooting.

E or V — Voltage

Voltage is electrical potential difference.

It is measured in volts.

I — Current

Current is the rate of electrical charge flow.

It is measured in amperes, or amps.

R — Resistance

Resistance is opposition to current flow.

It is measured in ohms.

Know the Symbols

In many electrical formulas, voltage is represented by E, current by I, and resistance by R.

You may also see voltage written as V.

The Three Forms of Ohm’s Law

Ohm’s Law can be rearranged depending on which value you are trying to find.

Find Voltage E = I × R

Find Current I = E ÷ R

Find Resistance R = E ÷ I

You do not need three known values.

You need two known values. Choose the form of Ohm’s Law that solves for the value you do not know.

The Ohm’s Law Triangle

Some students find this triangle useful as a memory aid.

E

I R

Cover the value you are trying to find.

If you cover E, the remaining values are:

I × R

If you cover I, the remaining relationship is:

E ÷ R

If you cover R, the remaining relationship is:

E ÷ I

Use the triangle as a memory aid, but understand the relationship instead of simply memorizing the picture.

WORKED EXAMPLE 1

Find the Voltage

Suppose a resistive load has:

Current 10 A

Resistance 10 Ω

We want to find voltage.

E = I × R

E = 10 × 10

E = 100 V

The voltage across the load is 100 volts.

WORKED EXAMPLE 2

Find the Resistance

Suppose a circuit has:

Voltage 120 V

Current 2 A

We want to find resistance.

R = E ÷ I

R = 120 ÷ 2

R = 60 Ω

The resistance is 60 ohms.

WORKED EXAMPLE 3

Find the Current

Suppose a simple resistive heating element has:

Voltage 240 V

Resistance 12 Ω

We want to find current.

I = E ÷ R

I = 240 ÷ 12

I = 20 A

In this ideal resistive example, the load current is 20 amps.

How the Values Affect Each Other

Ohm’s Law becomes much more useful when you understand the relationships instead of only calculating answers.

Resistance Stays the Same Increase voltage → current increases Decrease voltage → current decreases

Voltage Stays the Same Increase resistance → current decreases Decrease resistance → current increases

Think about the relationship.

If the electrical pressure increases while resistance remains the same, more current flows.

If resistance increases while voltage remains the same, less current flows.

Do not use simple resistance measurements to size an HVAC breaker.

Ohm’s Law works directly for simple resistive examples such as the problems on this page.

Motors, compressors, capacitors, transformers and other AC loads are not always simple fixed resistances.

HVAC branch-circuit conductor and overcurrent-protection sizing must be based on the equipment ratings, nameplate information, applicable instructions and electrical-code requirements.

Where Ohm’s Law Helps in Troubleshooting

Checking Resistive Loads

If you know the voltage and resistance of a simple resistive load, you can estimate the current it should draw.

Checking Resistance

If you know the voltage and current in an appropriate resistive circuit, you can calculate the effective resistance.

Understanding Faults

A large decrease in resistance can cause a large increase in current when the applied voltage remains the same.

Understanding Meter Readings

Ohm’s Law helps you decide whether voltage, current and resistance measurements make sense together.

Practice Problems

Work these out before looking at the answers.

Problem 1

A load has 24 volts across it and a resistance of 12 ohms.

What is the current?

Problem 2

A load draws 3 amps and has a resistance of 40 ohms.

What voltage is across the load?

Problem 3

A circuit has 120 volts across a load and the load draws 5 amps.

What is the resistance?

Show Answers

Problem 1:
I = E ÷ R
I = 24 ÷ 12
I = 2 A

Problem 2:
E = I × R
E = 3 × 40
E = 120 V

Problem 3:
R = E ÷ I
R = 120 ÷ 5
R = 24 Ω

Rules to Remember

1 E or V represents voltage.

2 I represents current.

3 R represents resistance.

4 E = I × R

5 I = E ÷ R

6 R = E ÷ I

7 At constant resistance, increasing voltage increases current.

8 At constant voltage, increasing resistance decreases current.

Glossary

Ohm’s Law: The relationship between voltage, current and resistance in a resistive circuit.
Voltage: Electrical potential difference between two points, measured in volts.
Current: The rate of electrical charge flow, measured in amperes.
Resistance: Opposition to current flow, measured in ohms.
Ohm: The unit used to measure electrical resistance. The symbol is Ω.
Ampere: The unit used to measure electrical current. It is commonly shortened to amp.

Do not just memorize the formulas.

Ask yourself what should happen when voltage changes. Ask what should happen when resistance changes.

Once you understand the relationship, Ohm’s Law becomes more than a math exercise. It becomes another tool for understanding what an electrical circuit is doing.

Ohm’s Law