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Ohm's Law

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Now the three ideas come together

We already know what voltage, current, and resistance mean. Ohm's law simply tells us how those three quantities relate for an ohmic resistance:

V = I × R

Reading Ohm's law

V = voltage, measured in volts (V)
I = current, measured in amperes (A)
R = resistance, measured in ohms (Ω)

So V = I × R reads: “voltage equals current times resistance.”

Reading the schematic: straight lines are wires; the unequal parallel lines are a cell/battery symbol; a zigzag is a resistor; a circle marked V is a voltmeter; a circle marked A is an ammeter. Labels beside the symbols tell us their values.
12 V 6 Ω I = 2 A

A useful first picture

More electrical “push” tends to produce more current. More opposition tends to produce less current. Ohm's law puts numbers to that idea.

Another way to think of this

Keep one quantity fixed and change another. If resistance stays the same and voltage doubles, current doubles. If voltage stays the same and resistance doubles, current is cut in half.

What is really happening?

Ohm's law is not a magical rule that every electrical device must obey. It describes the linear relationship between voltage and current for an ohmic conductor under the conditions where its resistance is effectively constant.

For basic DC resistor circuits, that is exactly the relationship we need.

Where did the name come from?

Georg Simon Ohm used experiments to study how current changed with the applied electrical conditions and conductor properties. His 1827 work eventually became foundational to circuit analysis, even though his ideas were not immediately appreciated by everyone.

Worked example

12 V 6 Ω I = ?

Question: A 12 V battery is connected across a 6 Ω resistor. Find current.

Step 1: Choose the form that solves for current:

I = V ÷ R

Step 2: Substitute the numbers:

I = 12 ÷ 6 = 2 A

Answer: 2 amperes.

Try these yourself

These are deliberately “state-test style”: simple arithmetic, one idea at a time, and no calculator should be necessary.

A 12 V source is connected across a 6 Ω resistor. What current flows? 12 V 6 Ω I = ?
I = V ÷ R = 12 ÷ 6 = 2 A.
A 4 Ω resistor carries 2 A. What voltage is across it? V = ? 4 Ω 2 A
V = I × R = 2 × 4 = 8 V.
A 10 V source causes 2 A to flow. What is the resistance? 10 V R = ? 2 A
R = V ÷ I = 10 ÷ 2 = 5 Ω.

A little deeper

The three useful forms are:

V = IR     I = V/R     R = V/I

Rather than memorizing three separate laws, remember that they are simply rearrangements of the same relationship.

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