Engineering · Electronics

Ohm's Law

Voltage Current Resistance Circuits

Ohm's Law is the single most important equation in electronics. It describes the relationship between voltage, current, and resistance in a circuit — and once you understand it, you can predict exactly what every component will do before you ever touch a wire.

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First: What Are Voltage, Current, and Resistance?

Before using the equation, get the three ideas straight. Voltage, current, and resistance are different parts of the same circuit story: the push, the flow, and what slows the flow down.

Voltage (Volts, V) Voltage is electrical pressure — the push that drives electrons through a circuit. A 9V battery has more push than a 1.5V AA cell. Without voltage, nothing moves. Named after Alessandro Volta.

Current (Amperes, A) Current is the flow of electric charge — how much charge passes a point each second. Think of it like the volume of water flowing through a pipe. The symbol is I, and small circuits often use milliamps (mA).

Resistance (Ohms, Ω) Resistance is opposition to current flow. A resistor acts like a narrow section of pipe: higher resistance means less current for the same voltage. Measured in ohms (Ω), named after Georg Ohm.

The Water Analogy Voltage is water pressure. Current is how fast the water flows. Resistance is how narrow the pipe is. A wider pipe (lower resistance) lets more water flow for the same pressure. A higher pressure (more voltage) pushes more water through the same pipe. This analogy breaks down eventually, but it makes the relationships intuitive.

Diagram showing the relationship between voltage, current, and resistance — Voltage, current, and resistance are connected: more voltage increases current, while more resistance reduces current.

What Is Ohm's Law?

In 1827, German physicist Georg Simon Ohm published a finding that changed electronics forever: the voltage across a conductor is directly proportional to the current flowing through it, as long as temperature stays constant. That relationship is written as one simple equation.

Portrait of German physicist Georg Simon Ohm — Georg Simon Ohm gave electronics one of its most useful relationships: voltage, current, and resistance move together in a predictable way.

Solve for Voltage V = I × R Voltage equals current times resistance

Solve for Current I = V ÷ R Current equals voltage divided by resistance

Solve for Resistance R = V ÷ I Resistance equals voltage divided by current

One Equation, Three Unknowns You only need to know two of the three values to find the third. If you know the voltage of your battery and the resistance of your component, you can calculate the exact current that will flow — before you even build the circuit.

Ohm's Law meme about voltage current and resistance — A quick memory hook for the relationship between voltage, current, and resistance.

Worked Examples

The best way to understand Ohm's Law is to use it. In every problem, identify what you know and which form of the equation you need.

Ex 1 LED with a current-limiting resistor

Situation: You have a 5V power supply and want to limit current through an LED to 20 mA (0.020 A). The LED drops about 2V across itself. How large a resistor do you need?

The voltage available for the resistor = 5V − 2V = 3V

Use R = V ÷ I

R = 3V ÷ 0.020A = 150 Ω

Answer: Use a 150 Ω resistor (or the next standard value up — 180 Ω — to keep the current safely below 20 mA).

Ex 2 Finding current in a simple circuit

Situation: A 9V battery is connected to a 470 Ω resistor. How much current flows?

Use I = V ÷ R

I = 9V ÷ 470Ω = 0.0191 A ≈ 19.1 mA

Answer: About 19 milliamps flow through the resistor.

Ex 3 Measuring an unknown resistance

Situation: You apply 12V to an unknown component and measure 40 mA (0.040 A) of current with a multimeter. What is its resistance?

Use R = V ÷ I

R = 12V ÷ 0.040A = 300 Ω

Answer: The component has a resistance of 300 Ω.

Ex 4 What voltage does a sensor need?

Situation: A sensor has an internal resistance of 2,200 Ω and needs exactly 5 mA (0.005 A) to operate correctly. What supply voltage does it need?

Use V = I × R

V = 0.005A × 2200Ω = 11V

Answer: The sensor needs an 11V supply to draw its rated 5 mA.

Power: The Fourth Quantity

Ohm's Law deals with V, I, and R — but there is a fourth quantity that goes hand in hand with it: Power (P), measured in Watts (W). Power is the rate at which a component converts electrical energy into heat, light, or motion.

Power from V and I P = V × I Watts = Volts × Amps

Power from I and R P = I² × R Watts = (Amps)² × Ohms

Power from V and R P = V² ÷ R Watts = (Volts)² ÷ Ohms

This matters because every component has a power rating. If more power flows through it than it is rated for, the component overheats and can fail — sometimes dramatically. A resistor rated for ¼ W will burn if you run ½ W through it.

Ex 5 Choosing a resistor by power rating

Situation: The 150 Ω LED resistor from Example 1 carries 20 mA at 3V. How much power does it dissipate? Is a standard ¼W resistor safe?

Use P = V × I

P = 3V × 0.020A = 0.06 W

Answer: 0.06 W — well under the ¼W (0.25W) rating. A standard resistor is fine. As a rule, keep components at or below 50% of their rated power for long-term reliability.

Why Resistors Get Hot Every resistor converts the electrical power it dissipates directly into heat. The higher the power, the hotter it gets. If you pick up a resistor and it's painfully hot, the power through it is too high — either increase resistance, lower voltage, or use a higher-wattage component.

Ohm's Law in Series and Parallel Circuits

Real circuits have more than one component. The way components are connected — in series (one after another) or in parallel (side by side) — changes how resistance, voltage, and current behave.

Series Circuits

In a series circuit, components share the same current. The total resistance is the sum of all individual resistances. Voltage is shared — each component gets a portion of the total.

Series Three resistors in series: 100 Ω + 220 Ω + 330 Ω, powered by 12V

Total resistance: R_total = 100 + 220 + 330 = 650 Ω

Current (same everywhere): I = 12V ÷ 650Ω = 18.5 mA

Voltage across 100 Ω: V = 0.0185A × 100Ω = 1.85V

Voltage across 220 Ω: V = 0.0185A × 220Ω = 4.07V

Voltage across 330 Ω: V = 0.0185A × 330Ω = 6.11V

Check: 1.85 + 4.07 + 6.11 ≈ 12V ✓ — the voltages always add up to the supply.

Parallel Circuits

In a parallel circuit, components share the same voltage. Each branch carries its own current. Total resistance goes down as you add more parallel branches — more paths for current to flow.

Parallel Two resistors in parallel: 300 Ω ∥ 600 Ω, powered by 6V

Total resistance: 1/R_total = 1/300 + 1/600 = 3/600 → R_total = 200 Ω

Total current from supply: I = 6V ÷ 200Ω = 30 mA

Current through 300 Ω branch: I = 6V ÷ 300Ω = 20 mA

Current through 600 Ω branch: I = 6V ÷ 600Ω = 10 mA

Check: 20 mA + 10 mA = 30 mA ✓ — branch currents always add up to the total.

Property	Series	Parallel
Current	Same through all components	Splits between branches
Voltage	Splits across components	Same across all branches
Total Resistance	Adds up (always increases)	Always less than smallest resistor
One branch opens	Entire circuit breaks	Other branches keep working
Common use	Voltage dividers, LED current limiting	House wiring, battery banks, power rails

Ohm's Law in the Real World

Every electronic device you own uses Ohm's Law — often thousands of times in a single circuit. Here are some places you will see it in action.

LED current limiting LEDs will draw as much current as a circuit can provide, and burn out instantly. A resistor calculated with Ohm's Law limits current to a safe value — typically 10–20 mA for standard LEDs.

Voltage dividers Two resistors in series split a voltage proportionally. This is how sensors like potentiometers and thermistors produce a variable analog voltage that a microcontroller can read.

Fuse sizing Fuses protect circuits by melting when current exceeds a safe limit. Engineers use Ohm's Law to predict the maximum current a circuit will draw, then choose a fuse just above that value.

Speaker impedance Speakers are rated in ohms (4Ω, 8Ω, 16Ω). An amplifier's output voltage and the speaker's impedance determine how much current the amplifier must supply — directly from V = IR.

Battery life estimation A 1000 mAh battery powering a circuit that draws 50 mA will last about 20 hours. Current draw is calculated from Ohm's Law; battery life follows from dividing capacity by draw.

USB power budgets USB ports supply 5V and are rated for a maximum current (500 mA for USB 2.0). When you plug in a device, the combined resistance of its circuits determines how much current it actually draws.

Common Mistakes

Forgetting to convert milliamps Ohm's Law requires consistent units. If your current is in milliamps (mA), divide by 1000 to get amps before plugging into the formula. 20 mA = 0.020 A.

Confusing voltage across a component with supply voltage In a series circuit, each component has its own voltage drop — not the full supply voltage. Always calculate the voltage across the specific component you care about.

Ignoring power ratings Calculating resistance with Ohm's Law is only half the job. Always check whether the power dissipated (P = I² × R) exceeds the component's wattage rating.

Treating LEDs like resistors LEDs do not obey Ohm's Law — they have a forward voltage drop that must be subtracted from the supply before calculating the current-limiting resistor value.

Adding parallel resistances like series ones Two 100 Ω resistors in series give 200 Ω. In parallel, they give 50 Ω. Always use the reciprocal formula (1/R_total = 1/R1 + 1/R2) for parallel combinations.

Using Ohm's Law for non-ohmic components Ohm's Law only applies to ohmic (linear) resistors. Capacitors, inductors, diodes, and transistors do not follow V = IR — they each have their own governing equations.

Quick Reference

Keep this table handy when working through circuit problems.

Find	Formula	You Need	Units
Voltage (V)	`V = I × R`	Current and Resistance	Volts (V)
Current (I)	`I = V ÷ R`	Voltage and Resistance	Amperes (A)
Resistance (R)	`R = V ÷ I`	Voltage and Current	Ohms (Ω)
Power (P)	`P = V × I`	Voltage and Current	Watts (W)
Power (P)	`P = I² × R`	Current and Resistance	Watts (W)
Series R_total	`R = R1 + R2 + …`	Each resistor value	Ohms (Ω)
Parallel R_total	`1/R = 1/R1 + 1/R2 + …`	Each resistor value	Ohms (Ω)

Quick Check

1. A resistor has a resistance of 40 Ω and 0.5 A of current flows through it. What is the voltage across it?

2. A 9V battery is connected to a 1,000 Ω (1 kΩ) resistor. How much current flows?

3. A component has 12V across it and draws 60 mA. What is its resistance?

4. Two resistors are connected in parallel across a 12V supply. What voltage appears across each resistor?

5. A 50 Ω resistor has 5V across it and carries 100 mA. How much power does it dissipate, and is a ¼W resistor safe?

6. You want to run an LED from a 5V supply at 15 mA. The LED has a forward voltage drop of 2V. What resistor do you need?