Ohm's Law

DC Circuits · 12 min read

Imagine connecting a resistor to a battery.

A 12 V battery pushes electric charges through the circuit. The resistor resists that movement. The result is a current flowing through the wire.

Figure 1. A battery (V) pushes current (I) through a resistor (R). This single circuit embodies Ohm's Law.

The relationship between these three quantities is called Ohm's Law:

V = I \cdot R

This simple equation is the foundation of electronics. Every LED circuit, sensor, Arduino project, amplifier, and power supply uses Ohm's Law in some way.

A Quick Experiment

Connect the same 10 Ω resistor to different voltages and record the current:

Voltage	Current
2 V	0.2 A
4 V	0.4 A
6 V	0.6 A

✅ Double the voltage → current doubles.

✅ Triple the voltage → current triples.

This is exactly what Georg Ohm discovered nearly 200 years ago.

Meet the Three Quantities

Voltage

V

The electrical push — created by a battery or power supply.

AA battery = 1.5 V
Car battery = 12 V
USB power = 5 V
Mains = 230 V

Analogy: water pressure in a pipe

Current

I

The flow of electric charge through the circuit.

LED = 20 mA
Phone charger = 1–3 A
Electric kettle = 8–12 A

Analogy: litres of water per second

Resistance

R

Opposes the flow of current.

Copper wire = < 0.01 Ω
Carbon resistor = 100 Ω – 1 MΩ
Insulation = > 100 MΩ

Analogy: a narrow section of pipe

Electrical Quantity	Water Analogy
Voltage (V)	Water pressure
Current (I)	Water flow rate (litres / sec)
Resistance (R)	Narrow pipe restriction

Increase pressure → more flow. Increase restriction → less flow.

The same relationship appears in Ohm's Law.

The Three Forms

One equation, rearranged three ways:

V = IR \qquad I = \dfrac{V}{R} \qquad R = \dfrac{V}{I}

Know V and R? → Use $I = V/R$
Know I and R? → Use $V = IR$
Know V and I? → Use $R = V/I$

= I × R

= V ∕ R

= V ∕ I

Figure 2. The Ohm's Law triangle — cover the quantity you want; what remains shows the formula.

Worked Example

A 12 V battery is connected to a 4 Ω resistor. How much current flows?

Write the known values: V = 12 V, R = 4 Ω
Choose the right form: we want I, so use $I = V / R$
Substitute: $I = 12 / 4$
Answer: I = 3 A

Current = 3 A. Every extra ohm of resistance reduces this. Every extra volt increases it.

Think Before Calculating

Predict the outcome first — then verify with Ohm's Law.

Scenario 1: Voltage doubles. Resistance stays the same. What happens to current?

Scenario 2: Resistance doubles. Voltage stays the same. What happens to current?

Scenario 3: Voltage doubles AND resistance doubles. What happens to current?

Common Mistakes

When Ohm's Law Applies

Ohm's Law works for ohmic components at constant temperature: fixed resistors, copper wire, carbon-film resistors.

Some devices are non-ohmic — their resistance changes with voltage, current, or temperature:

Beyond Ohm's Law: Power

Once you know V and I, you can find how much energy is converted per second:

P = V \cdot I

This leads directly into the next topic — Electrical Energy and Power.

Ohm's Playground

Drag the sliders — watch current and power update instantly.

Voltage12.0 V

1 V24 V

Resistance100 Ω

1 Ω1 kΩ

Current (I = V/R)

120.00 mA

Power (P = VI)

1.44 W

V vs I — R = 100 Ω

✅ Voltage is the electrical push (V)
✅ Current is the flow of charge (I)
✅ Resistance opposes current (R)
✅ Increasing V increases I (R constant)
✅ Increasing R decreases I (V constant)
✅ The master equation: $V = IR$