Ohm's Law for Beginners: V = IR Explained with Worked Examples
Ohm's Law is the fundamental relationship between voltage, current, and resistance in electrical circuits. Learn the formula, understand what each variable means physically, and see worked examples for common electronics calculations.
What Is Ohm's Law?
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across those points, provided the resistance is constant:
V = I × R
Where:
- V = Voltage in volts (V)
- I = Current in amperes (A)
- R = Resistance in ohms (Ω)
This simple relationship, discovered by Georg Ohm in 1827, underpins the analysis of virtually every electrical circuit.
The Three Forms of Ohm's Law
Rearranging the formula gives you three ways to use it:
V = I × R → find voltage
I = V / R → find current
R = V / I → find resistance
The VIR triangle is a memory aid: cover the quantity you want to find, and the remaining two show what to calculate.
The Power Formula
Combining Ohm's Law with the power equation P = V × I gives additional forms:
P = V × I
P = I² × R
P = V² / R
Where P is power in watts (W). These four variables (V, I, R, P) are related — knowing any two lets you calculate the other two.
Worked Examples
Example 1: Find the current through a resistor
A 100Ω resistor is connected to a 5V supply. What is the current?
I = V / R = 5V / 100Ω = 0.05 A = 50 mA
Example 2: Find the voltage drop across a resistor
A 2.2kΩ resistor carries 1mA of current. What is the voltage across it?
V = I × R = 0.001 A × 2200 Ω = 2.2 V
Example 3: Find the resistance
An LED circuit runs from 5V and has a measured current of 20mA. What resistance is in the circuit?
R = V / I = 5V / 0.02A = 250 Ω
Example 4: Power dissipation
A 470Ω resistor carries 30mA. Does it exceed a ¼W (0.25W) rating?
P = I² × R = (0.03)² × 470 = 0.423 W
Yes — this exceeds a quarter-watt resistor's rating. Use a ½W or 1W resistor.
Units and Prefixes
Electronics uses SI prefixes extensively. Key ones to know:
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| mega | M | × 10⁶ | 2 MΩ (2 megaohm) |
| kilo | k | × 10³ | 4.7 kΩ (4700 Ω) |
| milli | m | × 10⁻³ | 20 mA (0.02 A) |
| micro | μ | × 10⁻⁶ | 100 μA (0.0001 A) |
| nano | n | × 10⁻⁹ | 5 nA |
When Ohm's Law Does NOT Apply
Ohm's Law applies to ohmic (linear) conductors — those where resistance is constant regardless of voltage or current.
Some components are non-ohmic:
- Diodes — current increases exponentially with forward voltage (governed by the Shockley equation)
- LEDs — similar to diodes, must be driven via a series resistor
- Transistors — variable resistance controlled by base current or gate voltage
- Incandescent bulbs — resistance increases with temperature (filament heats up)
- NTC thermistors — resistance decreases with temperature
For these components, Ohm's Law gives only an approximation at a specific operating point.
Series and Parallel Resistors
Series — resistors in series add directly:
R_total = R1 + R2 + R3
Parallel — the reciprocal rule:
1 / R_total = 1/R1 + 1/R2 + 1/R3
For two resistors in parallel, the simplified form is:
R_total = (R1 × R2) / (R1 + R2)