One simple equation
In 1827, German physicist Georg Ohm discovered a simple rule connecting the three most important quantities in an electric circuit. Ohm’s law is used every day by electricians, engineers and anyone designing electronics.
The three quantities
| Quantity | Symbol | Unit | Measured with |
|---|---|---|---|
| Voltage | V | volt (V) | Voltmeter |
| Current | I | ampere, or amp (A) | Ammeter |
| Resistance | R | ohm (Ω) | Ohmmeter |
The symbol for current is I, from the French intensité.
The water pipe analogy
| Electricity | Water |
|---|---|
| Voltage | Water pressure from a pump |
| Current | How much water flows per second |
| Resistance | How narrow the pipe is |
More pressure pushes more water. A narrower pipe lets less water through.
Ohm’s law
V = I × R
You can rearrange it to find any of the three:
| To find | Formula |
|---|---|
| Voltage | V = I × R |
| Current | I = V ÷ R |
| Resistance | R = V ÷ I |
The Ohm’s law triangle
Draw a triangle with V at the top and I and R side by side at the bottom. Cover the one you want:
- Cover V → I × R
- Cover I → V ÷ R
- Cover R → V ÷ I
Worked examples
Example 1: Find the current. A 9 V battery is connected to a 3 Ω resistor.
I = V ÷ R = 9 ÷ 3 = 3 A
Example 2: Find the voltage. A current of 0.5 A flows through a 24 Ω bulb.
V = I × R = 0.5 × 24 = 12 V
Example 3: Find the resistance. A toaster draws 10 A from a 120 V outlet.
R = V ÷ I = 120 ÷ 10 = 12 Ω
What the law tells us
| Change | Effect on current |
|---|---|
| Double the voltage (same resistance) | Current doubles |
| Double the resistance (same voltage) | Current halves |
Graphing voltage against current for a resistor gives a straight line through the origin. Its slope equals the resistance. A conductor that behaves like this is called ohmic.
Not everything is ohmic. A light bulb filament gets hotter as current rises, and its resistance increases, so its graph curves.
What affects resistance?
| Factor | Effect |
|---|---|
| Material | Copper has low resistance; nichrome (used in toasters) has high resistance |
| Length | Longer wire → more resistance |
| Thickness | Thinner wire → more resistance |
| Temperature | Hotter metal → more resistance |
Think of a crowd leaving a stadium: a long, narrow hallway slows people down more than a short, wide one.
Resistors
A resistor is a component that adds a set amount of resistance. Resistors control current to protect sensitive parts. For example, an LED needs a resistor so it doesn’t burn out.
Small resistors are marked with coloured bands that tell their value.
Electrical power
Ohm’s law connects to power:
P = V × I
Combining with Ohm’s law gives P = I² × R and P = V² ÷ R.
Example: The 120 V toaster drawing 10 A uses P = 120 × 10 = 1200 W.
Ohm’s law and safety
Your body has resistance, mostly from dry skin. Wet skin has much lower resistance, so the same voltage pushes much more current through you. That’s why electricity near water is so dangerous. Even a small current through the heart (about 0.1 A) can be deadly.
Common mistakes
- Mixing up the units. Volts for voltage, amps for current, ohms for resistance.
- Forgetting to convert milliamps. 250 mA = 0.25 A.
- Assuming every device is ohmic.
Try it yourself
- A 6 V battery powers a 2 Ω motor. What is the current?
- A 100 Ω resistor carries 0.2 A. What is the voltage across it?
- A phone charger supplies 5 V and 2 A. What is the resistance of the load? What power does it deliver?
- If you double the voltage across a 10 Ω resistor from 5 V to 10 V, what happens to the current?
(Answers: 3 A; 20 V; 2.5 Ω and 10 W; it doubles from 0.5 A to 1 A)
Quick recap
- Voltage pushes current through resistance.
- Ohm’s law: V = I × R.
- More voltage means more current; more resistance means less.
- Resistance depends on material, length, thickness and temperature.
- Power = V × I.