Ohm's law

What you’ll learn

Ohm’s law: V = I × R
How to rearrange it to find any one value
Power: P = V × I, and why parts get hot

The equation

V = I × R

Voltage (volts) = Current (amps) × Resistance (ohms)

Rearranged:

You want	Formula
Voltage	V = I × R
Current	I = V ÷ R
Resistance	R = V ÷ I

Power and heat

Every component that resists current turns some energy into heat. Power is measured in watts (W):

P = V × I

Example: a resistor has 5 V across it and 0.02 A through it. P = 5 × 0.02 = 0.1 W. Standard small resistors are rated for 0.25 W, so that’s fine.

If the power is more than the part’s rating, it overheats. This is why short circuits are dangerous: R is almost 0, so I becomes huge.

Example: a sensor’s pull-up resistor

A 10 kΩ resistor connects a button input to 5 V. How much current flows when the button is pressed (connecting the pin to GND)?

I = V ÷ R = 5 ÷ 10,000 = 0.0005 A = 0.5 mA, tiny, which is why 10 kΩ is a popular pull-up value.

Example: a motor coil

A small motor coil has 12 Ω of resistance and runs on 6 V. When stalled (not spinning), current is I = 6 ÷ 12 = 0.5 A, and the power is P = 6 × 0.5 = 3 W. A stalled motor gets hot.

Example: choosing a resistor wattage

A resistor drops 9 V with 30 mA through it: P = 9 × 0.03 = 0.27 W. That’s more than a standard 0.25 W resistor can handle, so use a 0.5 W resistor.

Worked examples

1. Find the current. A 9 V battery is connected across a 1,000 Ω (1 kΩ) resistor.

I = V ÷ R = 9 ÷ 1000 = 0.009 A = 9 mA

2. Find the resistance. You want 20 mA (0.02 A) from a 5 V supply.

R = V ÷ I = 5 ÷ 0.02 = 250 Ω

3. Find the voltage. 0.5 A flows through a 10 Ω resistor.

V = I × R = 0.5 × 10 = 5 V