Last Updated: September 2, 2026
Quick Summary
Ohm’s Law describes the relationship between voltage, current, and resistance in an electrical circuit. The main equation is V = IR. By rearranging it, you get the three common Ohm’s Law formulas: V = IR, I = V/R, and R = V/I.
This guide explains how to use each formula, calculate voltage, current, and resistance, understand ohmic and non-ohmic components, and solve series and parallel circuit problems.
Key Takeaways
- The main Ohm’s Law formula is V = IR.
- The three forms are V = IR, I = V/R, and R = V/I.
- Voltage is measured in volts (V).
- Current is measured in amperes (A).
- Resistance is measured in ohms (Ω).
- Use I = V/R to find current.
- Use R = V/I to find resistance.
- Ohm’s Law applies to ohmic conductors when physical conditions such as temperature remain constant.
- In a series circuit, resistances add directly.
- In a parallel circuit, the reciprocal resistances add.
- Ohm’s Law is useful for physics problems, electronics, electrical engineering, automotive systems, and circuit analysis.
Who Is This Guide For?
This guide is designed for high school and college physics students, including GCSE, IGCSE, A-Level, and introductory electrical engineering students. It is useful for exam preparation, homework, laboratory work, circuit calculations, and practical electronics problems involving voltage, current, resistance, and series-parallel circuits.
It is also useful for electronics technicians, electrical engineering students, and STEM learners who need a quick way to calculate unknown circuit values and understand how resistors affect current and voltage.
What Is Ohm’s Law?
Ohm’s Law describes the relationship between voltage, current, and resistance in an electrical circuit.
The primary equation is:
V = IR
This means that voltage equals current multiplied by resistance.
For an ohmic conductor at constant temperature, current is proportional to voltage. If resistance remains constant and voltage increases, current increases proportionally.
For example, if a 10 Ω resistor carries a current of 2 A:
V = IR
V = 2 × 10
V = 20 V
So the voltage across the resistor is 20 V.
Ohm’s Law is one of the most useful relationships in basic circuit analysis because it allows you to calculate any one of the three variables when the other two are known.
The Three Forms of Ohm’s Law
The three common forms of Ohm’s Law come from rearranging the same equation:
1. Voltage Formula: V = IR
Use this form when you know current and resistance and need to find voltage.
V = IR
Where:
- V = voltage in volts (V)
- I = current in amperes (A)
- R = resistance in ohms (Ω)
2. Current Formula: I = V/R
Use this form when you know voltage and resistance and need to find current.
I = V/R
For example, a 12 V source connected to a 6 Ω resistor produces:
I = 12/6
I = 2 A
So the current is 2 A.
3. Resistance Formula: R = V/I
Use this form when voltage and current are known but resistance is unknown.
R = V/I
For example, if a circuit has 24 V and a current of 3 A:
R = 24/3
R = 8 Ω
So the circuit resistance is 8 Ω.
Ohm’s Law Formula Triangle
A useful way to remember the three forms is to think of the relationship as a formula triangle:
V
I × R
Cover the variable you want to find:
- Cover V → V = IR
- Cover I → I = V/R
- Cover R → R = V/I
This method is particularly useful for students solving basic circuit formulas under exam conditions.
Understanding Voltage, Current, and Resistance
Voltage
Voltage is the electrical potential difference between two points.
It provides the potential energy difference that drives charge through a circuit.
Voltage is measured in volts (V).
Common voltage sources include batteries, power supplies, and generators.
Current
Electric current is the rate at which electric charge flows through a circuit.
Current is measured in amperes (A).
The basic current equation is:
I = Q/t
where:
- I = current
- Q = electric charge
- t = time
Resistance
Resistance is the opposition to the flow of electric current.
Resistance is measured in ohms (Ω).
A larger resistance generally produces a smaller current for the same applied voltage.
This relationship can be seen directly from:
I = V/R
If voltage stays constant and resistance increases, current decreases.
Ohm’s Law Units
The SI units used in Ohm’s Law are:
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | V | Volt (V) |
| Current | I | Ampere (A) |
| Resistance | R | Ohm (Ω) |
From:
V = IR
we can also write:
1 Ω = 1 V/A
This means one ohm is equivalent to one volt per ampere.
Solved Ohm’s Law Examples
Example 1: Find Current
A 9 V battery is connected to a 3 Ω resistor. Find the current.
Given:
V = 9 V
R = 3 Ω
Formula:
I = V/R
Calculation:
I = 9/3
I = 3 A
Therefore, the current is 3 A.
Example 2: Find Voltage
A current of 2 A flows through a resistor with a resistance of 5 Ω. Find the voltage.
Given:
I = 2 A
R = 5 Ω
Formula:
V = IR
Calculation:
V = 2 × 5
V = 10 V
Therefore, the voltage is 10 V.
Example 3: Find Resistance
A circuit has a voltage of 12 V and a current of 0.4 A. Find the resistance.
Given:
V = 12 V
I = 0.4 A
Formula:
R = V/I
Calculation:
R = 12/0.4
R = 30 Ω
Therefore, the resistance is 30 Ω.
How to Find Current
To find current when voltage and resistance are known, use:
I = V/R
The steps are:
- Identify the voltage.
- Identify the resistance.
- Divide voltage by resistance.
- Express the answer in amperes.
For example:
V = 20 V
R = 10 Ω
Therefore:
I = 20/10 = 2 A
So the current is 2 A.
How to Find Resistance
To find resistance, use:
R = V/I
For example, if a circuit operates at 18 V and carries 3 A:
R = 18/3
R = 6 Ω
Therefore, the resistance is 6 Ω.
This form of Ohm’s Law is commonly used when experimental measurements of voltage and current are available.
How to Find Voltage
To find voltage, use:
V = IR
For example, a resistor carries 4 A and has a resistance of 8 Ω:
V = 4 × 8
V = 32 V
Therefore, the voltage is 32 V.
Ohmic and Non-Ohmic Conductors
Ohm’s Law does not apply equally to every electrical component under all conditions.
An ohmic conductor has a constant resistance under constant physical conditions. Its current-voltage relationship is approximately linear.
Examples can include suitable metallic conductors operating under controlled conditions.
A non-ohmic component does not maintain a constant resistance as voltage or current changes.
Examples include components such as diodes and LEDs, where the current-voltage relationship is not simply linear.
Temperature can also affect resistance. In metallic conductors, resistance generally increases as temperature increases.
Ohm’s Law and Series Circuits
In a series circuit, components are connected along a single continuous path.
The current is the same through each component:
Iₜₒₜₐₗ = I₁ = I₂ = I₃
The total resistance is:
Rₜₒₜₐₗ = R₁ + R₂ + R₃
The total voltage is divided across the components:
Vₜₒₜₐₗ = V₁ + V₂ + V₃
Series Circuit Example
Three resistors of:
2 Ω, 4 Ω, and 6 Ω
are connected in series.
Total resistance:
Rₜₒₜₐₗ = 2 + 4 + 6
Rₜₒₜₐₗ = 12 Ω
If the supply voltage is 24 V:
I = V/R
I = 24/12
I = 2 A
Therefore, the circuit current is 2 A.
Ohm’s Law and Parallel Circuits
In a parallel circuit, components are connected across the same two nodes.
The voltage is the same across each parallel branch:
Vₜₒₜₐₗ = V₁ = V₂ = V₃
The total current is the sum of the branch currents:
Iₜₒₜₐₗ = I₁ + I₂ + I₃
For parallel resistors:
1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + 1/R₃
The equivalent resistance of a parallel circuit is always lower than the smallest individual resistance.
Parallel Circuit Example
Two resistors of 6 Ω and 12 Ω are connected in parallel across a 12 V supply.
First calculate the equivalent resistance:
1/Rₜₒₜₐₗ = 1/6 + 1/12
1/Rₜₒₜₐₗ = 2/12 + 1/12
1/Rₜₒₜₐₗ = 3/12
Therefore:
Rₜₒₜₐₗ = 4 Ω
Now calculate the total current:
Iₜₒₜₐₗ = V/R
Iₜₒₜₐₗ = 12/4
Iₜₒₜₐₗ = 3 A
Therefore, the total current is 3 A.
Complex Series-Parallel Circuits
Many practical circuits contain both series and parallel resistors.
A useful strategy is to simplify the circuit step by step.
Step-by-Step Method
- Identify resistors connected in parallel.
- Calculate their equivalent resistance.
- Replace the parallel group with its equivalent resistance.
- Combine remaining series resistances.
- Continue until you have one total resistance.
- Use I = V/R to calculate total current.
- Work backward through the circuit to calculate individual voltages and currents.
Series-Parallel Example
A 12 V battery is connected to a 6 Ω resistor in series with a parallel combination of 4 Ω and 12 Ω.
First calculate the parallel resistance:
R₂₃ = (4 × 12)/(4 + 12)
R₂₃ = 48/16
R₂₃ = 3 Ω
Now add the series resistor:
Rₜₒₜₐₗ = 6 + 3
Rₜₒₜₐₗ = 9 Ω
Total current:
I = 12/9
I ≈ 1.33 A
Voltage across the parallel group:
V = IR
V = 1.33 × 3
V ≈ 4 V
Current through the 4 Ω resistor:
I = 4/4 = 1 A
Current through the 12 Ω resistor:
I = 4/12 ≈ 0.33 A
The branch currents add to approximately:
1 A + 0.33 A = 1.33 A
which agrees with the total circuit current.
Ohm’s Law and Electrical Power
Ohm’s Law can also be combined with the electrical power equation:
P = VI
Using:
V = IR
you can derive:
P = I²R
and:
P = V²/R
Therefore, the three useful electrical power formulas are:
P = VI
P = I²R
P = V²/R
where P is electrical power measured in watts (W).
These relationships are useful when analyzing resistor power dissipation and selecting suitable electrical components.
When Should You Use Ohm’s Law?
Use Ohm’s Law whenever you need to determine an unknown voltage, current, or resistance in a circuit and the required two quantities are known.
In education, it is commonly used for physics exams, homework, laboratory measurements, and circuit-analysis exercises. In electrical and electronics applications, it helps technicians and engineers estimate circuit current, select resistors, check voltage drops, analyze loads, and understand how changes in resistance affect current.
Ohm’s Law is especially useful when making circuit-design decisions, such as determining whether a resistor provides the desired current or checking whether a component will operate within its expected electrical conditions.
Real-World Applications of Ohm’s Law
Ohm’s Law is used in many practical electrical and electronic systems.
Electronics
Engineers and electronics technicians use Ohm’s Law to calculate resistor values, current levels, and voltage drops in electronic circuits.
Automotive Electrical Systems
Vehicle electrical systems contain batteries, lights, motors, sensors, and other loads. Ohm’s Law can help analyze voltage, current, and resistance relationships in these circuits.
LED Circuits
A resistor is often used with an LED to control current. Ohm’s Law can help determine an appropriate resistance when the supply voltage and desired current are known.
Electrical Engineering
Ohm’s Law is one of the basic tools used in electrical circuit analysis and is combined with other circuit principles to study more complex systems.
For additional electricity and circuit formulas, see the Electricity & Magnetism study notes on Simple Physics Lab. The page covers Ohm’s Law, current, voltage, resistance, series and parallel circuits, and related electromagnetic topics.
For a broader collection of equations, see the Physics Formulas List, which includes Ohm’s Law, electrical power, current, electric field, and other physics formulas.
Interactive Ohm’s Law Simulation
An interactive simulation can make the relationship between voltage, current, and resistance easier to visualize.
The PhET Ohm’s Law Simulation allows you to change voltage and resistance and observe how the circuit and Ohm’s Law equation respond.
For a broader circuit activity, the PhET Circuit Construction Kit: DC covers Ohm’s Law along with series and parallel circuits and allows learners to build circuits and take current and voltage measurements.
For a textbook reference, see OpenStax: Ohm’s Law, Resistance and Simple Circuits. It covers calculating voltage, current, resistance, and understanding ohmic materials and simple circuits.
Frequently Asked Questions About Ohm’s Law
What are the 3 forms of Ohm’s Law?
The three common forms of Ohm’s Law are:
V = IR
I = V/R
R = V/I
They are different arrangements of the same relationship between voltage, current, and resistance.
What are the 3 Ohm’s Law formulas used to find?
V = IR finds voltage.
I = V/R finds current.
R = V/I finds resistance.
Choose the equation based on the quantity you need to calculate.
What is the Ohm’s Law formula?
The primary Ohm’s Law equation is:
V = IR
Voltage equals current multiplied by resistance.
How do you find current using Ohm’s Law?
Use:
I = V/R
Divide the voltage by the resistance.
For example, a 10 V supply connected to a 5 Ω resistor gives:
I = 10/5 = 2 A
How do you find resistance using Ohm’s Law?
Use:
R = V/I
Divide voltage by current.
For example:
R = 12 V/2 A = 6 Ω
How do you find voltage using Ohm’s Law?
Use:
V = IR
Multiply current by resistance.
For example:
V = 3 A × 4 Ω = 12 V
What is an ohmic conductor?
An ohmic conductor maintains approximately constant resistance under constant physical conditions and has a linear relationship between voltage and current.
What is the difference between series and parallel circuits?
In a series circuit, the same current flows through each component and resistances add directly.
In a parallel circuit, the same voltage appears across each branch, current divides between branches, and the equivalent resistance is calculated using reciprocal resistance.
What happens to current when resistance increases?
If voltage remains constant, increasing resistance decreases current.
This follows directly from:
I = V/R
For example, if voltage stays at 12 V, increasing resistance from 3 Ω to 6 Ω reduces current from 4 A to 2 A.
What causes a short circuit?
A short circuit provides an unintended path with very low resistance. Because:
I = V/R
a very small resistance can produce a very large current if the voltage source can supply it. This can cause overheating, component damage, or fire.
Is Ohm’s Law valid for every electrical component?
No. Ohm’s Law in its simple proportional form applies to ohmic conductors under appropriate constant conditions. Some components, such as diodes and LEDs, have non-linear current-voltage relationships.
Ohm’s Law Formula Summary
The three essential formulas are:
V = IR
I = V/R
R = V/I
For circuit analysis, also remember:
Series:
Rₜₒₜₐₗ = R₁ + R₂ + R₃
Parallel:
1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + 1/R₃
For electrical power:
P = VI
P = I²R
P = V²/R
Together, these equations provide the foundation for solving many basic voltage, current, resistance, power, and circuit-analysis problems.
Final Takeaway
Ohm’s Law provides a simple way to connect the three fundamental circuit quantities: voltage, current, and resistance. Start with V = IR, then rearrange it depending on the quantity you need.
If you remember these three forms—
V = IR
I = V/R
R = V/I
you can solve most introductory Ohm’s Law calculations and then extend the same principles to series, parallel, and more complex electrical circuits.