Ohm's Law

The Equation

V = I × R

• V — Voltage in Volts (V)
• I — Current in Amperes (A)
• R — Resistance in Ohms (Ω)

Three forms, depending on what you’re solving for:

V = I × R      (voltage across a resistor)
I = V / R      (current through a resistor)
R = V / I      (resistance from measurements)

Named after Georg Simon Ohm, who published it in 1827 and was initially ridiculed for it.

Intuition

I find the water analogy useful:

• Voltage = water pressure
• Current = flow rate (litres per second)
• Resistance = how narrow the pipe is

High pressure + narrow pipe = some flow. Wide pipe = lots of flow at the same pressure. Pump harder = more flow through the same pipe.

The analogy breaks down at high frequencies and with reactive components, but for DC and resistive circuits it maps cleanly.

Ohmic vs Non-Ohmic Components

Ohm’s Law strictly applies to ohmic materials — where resistance stays constant regardless of voltage or current. Most resistors are ohmic.

Many components are non-ohmic — their resistance changes with conditions:

• LEDs and diodes: resistance drops dramatically once forward voltage is exceeded. Current spikes. This is why they always need a series resistor.
• Transistors: resistance between collector and emitter is controlled by base current.
• Light-dependent resistors (LDRs): resistance changes with light intensity.
• Thermistors: resistance changes with temperature.

Kirchhoff’s Laws

Ohm’s Law handles one component. Kirchhoff’s Laws handle entire circuits.

KVL — Kirchhoff’s Voltage Law: The sum of all voltages around any closed loop equals zero. Voltage rises (sources) equal voltage drops (resistors, LEDs, etc.).

In a series circuit: Vsupply = V_R1 + V_R2 + V_LED
9V = 3V + 4V + 2V ✓

KCL — Kirchhoff’s Current Law: The sum of currents entering a node equals the sum leaving. Current doesn’t pile up anywhere.

In a parallel circuit: I_total = I_branch1 + I_branch2

Working Through a Real Problem

Problem: I have a 12V supply and want to run two red LEDs (Vf = 2V each, If = 15mA) in series from it.

1. Total forward voltage of LEDs in series: 2V + 2V = 4V
2. Voltage across resistor: 12V − 4V = 8V
3. Current (same through series circuit): 15mA = 0.015A
4. R = V/I = 8V / 0.015A = 533Ω → use 560Ω (nearest E12 value)
5. Power in resistor: P = I²R = (0.015)² × 560 = 0.126W → ¼W resistor is fine

This calculation runs before every circuit I build now.

Power Formula

Power is related to the other three quantities:

P = V × I        (power = voltage × current)
P = I² × R       (power dissipated as heat in a resistor)
P = V² / R

Unit: Watts (W). A 9V battery at 100mA delivers 0.9W. Always check that components can handle the power dissipation.

The Big Picture

Ohm’s Law is the first tool you reach for. Every circuit analysis starts here — find the unknowns, set the operating point, choose component values. It’s as fundamental to electronics as F = ma is to mechanics.