Ohm's Law

The Three Quantities

Quantity	Symbol	Unit	Measured with
Voltage	V	Volt (V)	Voltmeter
Current	I	Ampere (A)	Ammeter
Resistance	R	Ohm (Ω)	Ohmmeter

Ohm's Law

Voltage

V = I \cdot R

Voltage = Current × Resistance

Current

I = \dfrac{V}{R}

Current = Voltage ÷ Resistance

Resistance

R = \dfrac{V}{I}

Resistance = Voltage ÷ Current

The VIR Triangle

A bulb has resistance 20 Ω and current 0.5 A flows through it. Find the voltage.

$V = I \times R = 0.5 \times 20 = 10 \text{ V}$

A 12 V battery powers a 6 Ω resistor. Find the current.

$I = \dfrac{V}{R} = \dfrac{12}{6} = 2 \text{ A}$

Real world: Choosing a fuse for a kitchen appliance

A toaster draws 4.6 A from a 230 V supply (P = 1060 W). Using Ohm's Law: R = V/I = 230/4.6 = 50 Ω. Knowing the current, an electrician selects a 5 A fuse (the next standard size above 4.6 A) to protect the circuit without interrupting normal use.

Real world: Why a longer USB cable charges your phone more slowly

A very long or thin USB cable has a higher total resistance. By Ohm's Law (I = V/R), a higher resistance reduces the current delivered to your phone's battery. You can feel the cable warming up — wasted energy being converted to heat in the cable's resistance instead of going into the battery.

Tip Where do you see Ohm's Law in real life? Every household appliance, smartphone charger, electric car battery, and circuit fuse relies on the relationship V = IR to operate safely and efficiently!

Practice Problems

A resistor has 9 V across it and 3 A through it. What is its resistance?

Show answer

R = V ÷ I = 9 ÷ 3 = 3 Ω.

A lamp has a resistance of 40 Ω. What current flows when connected to 240 V?

Show answer

I = 240 ÷ 40 = 6 A.