Ohm's Law — V = IR Explained with Circuits and Examples

High School⏱ 9 min readElectricity & Magnetism

Ohm's law V = IR: voltage, current and resistance. What each means, when the law holds, and worked circuit examples.

Quick answer

Ohm's law says current through a conductor is proportional to the voltage across it: V = IR. Voltage pushes, resistance opposes, current is the resulting flow.

$V = IR$

Unit: volts (V) = amps (A) × ohms (Ω)

Example: A 12 V battery across a 4 Ω bulb drives I = 12/4 = 3 A of current — tripling the voltage would triple the current.

What you will learn

Define voltage, current and resistance
Apply V = IR to solve circuit problems
Distinguish ohmic from non-ohmic behavior
Explain current, voltage and resistance intuitively

The three quantities

Three quantities run every circuit:

Voltage ( $V$ ): the electrical 'push' — energy per unit charge, supplied by batteries or wall outlets.
Current ( $I$ ): the flow rate of charge — coulombs per second.
Resistance ( $R$ ): how much the material opposes the flow.

A water analogy helps: voltage is pump pressure, current is flow rate, resistance is a narrow pipe section. More pressure or a wider pipe both increase flow.

The law: V = IR

For ohmic materials, current is directly proportional to voltage:

V = IR

V in volts, I in amps, R in ohms

Current I flows from + to − through the resistor R, driven by voltage V.

What resistance really is

Resistance measures opposition to current. Causes:

Material: copper's resistance is tiny; rubber's is astronomical.
Length: longer wire, more resistance (more collisions).
Thickness: wider wire, less resistance (more lanes).
Temperature: hotter metals resist more (atoms jiggle harder).

$R = \rho\frac{L}{A}$

with resistivity $\rho$ characterizing the material. Superconductors — zero resistance below a critical temperature — are the exotic exception.

Ohmic vs non-ohmic

Ohm's law is a behavior, not a commandment:

Ohmic: metals at steady temperature — straight-line V-I graph through the origin. V = IR holds.
Non-ohmic: filament bulbs (resistance rises as they heat), diodes (conduct one way), LEDs, transistors.

A bulb's filament heats to ~2500 °C as current flows, raising its resistance tenfold from cold. Its V-I curve bends — Ohm's law, strictly, fails. Engineers still use V = IR instantaneously, with the hot resistance.

Key idea

V = IR always relates the three quantities at one instant. 'Ohm's law' as a law additionally claims R stays constant — true for metals, false for bulbs and diodes.

Worked mini-example

A 9 V battery connects across a $27\ \Omega$ resistor. Find the current and the power dissipated.

$I = \frac{V}{R} = \frac{9}{27} = 0.33\ \mathrm{A}$

Power: $P = VI = 9 \times 0.33 = 3.0\ \mathrm{W}$ (equivalently $V^2/R = 81/27 = 3\ \mathrm{W}$ ✓). That 3 W becomes heat — which is why resistors in real circuits get warm.

Variables and units

Symbol	Name	Unit	Meaning
$V$	Voltage	V	Energy per unit charge driving the current
$I$	Current	A	Rate of charge flow
$R$	Resistance	Ω	Opposition to current flow

Common mistakes

✗ Current gets 'used up' by bulbs and resistors.

Charge is conserved — the same current flows before and after every component in series. What gets 'used' is energy, delivered as charge drops through voltage.

✗ More resistance means more current, since V = IR.

For a fixed voltage, current is V/R — more resistance means less current. The formula relates the three; it doesn't say which causes which.

✗ Ohm's law is a universal law of nature.

It's a material behavior (like Hooke's law for springs), valid for ohmic conductors. Many real devices — diodes, transistors, glowing filaments — disobey it.

Real-world applications

Fuses and breakers are rated in amps: exceed the wire's safe current and the fuse melts first, protecting the circuit.
Phone chargers convert wall voltage to a precise 5 V (or negotiated higher) that the battery can safely accept.
Household wiring is sized by expected current — high-draw appliances get thicker wire (lower resistance) to avoid overheating.

Frequently asked questions

What is an amp, intuitively?

The ampere (A) — one coulomb of charge passing per second. A phone charging at 2 A moves 2 coulombs through the cable every second.

Does Ohm's law apply to everything?

No. It holds for 'ohmic' materials (most metals at constant temperature). Filament bulbs, diodes, and semiconductors are non-ohmic — their resistance changes with voltage or temperature.

How does Ohm's law relate to electric power?

P = VI — power is voltage times current. Double the voltage across a fixed resistor and the power quadruples (since current doubles too): P = V²/R.

What happens to current when I add resistors?

In series, resistances add (R_total = R₁ + R₂) so current drops. In parallel, the equivalent resistance drops below any single branch, so total current rises.