The Foundation of Circuit Analysis
Ohm's Law is the single most used relationship in electronics and electrical engineering. It describes how voltage (V), current (I), and resistance (R) are related in a resistive circuit, and — extended with Joule's Law — how power (P) ties into the picture. Mastering these four quantities and their interrelationships allows you to analyse, design, and troubleshoot virtually any DC circuit.
The Four Core Formulas
| Find | Formula | Units |
|---|---|---|
| Voltage (V) | V = I × R | Volts (V) |
| Current (I) | I = V / R | Amperes (A) |
| Resistance (R) | R = V / I | Ohms (Ω) |
| Power (P) | P = V × I = I² × R = V² / R | Watts (W) |
How to Use This as a Calculator
You always need to know two of the four quantities to calculate the other two. Here's the decision process:
- Know V and R? → I = V/R and P = V²/R
- Know V and I? → R = V/I and P = V×I
- Know I and R? → V = I×R and P = I²×R
- Know P and V? → I = P/V and R = V²/P
- Know P and I? → V = P/I and R = P/I²
- Know P and R? → V = √(P×R) and I = √(P/R)
Worked Examples
Example 1: Calculating LED Current-Limiting Resistor
You want to run a red LED from a 5V supply. The LED has a forward voltage of 2.0V and requires 20mA. What resistor do you need?
- Voltage across resistor = Supply − LED Vf = 5.0 − 2.0 = 3.0V
- Required current = 20mA = 0.02A
- R = V / I = 3.0 / 0.02 = 150Ω
- Power in resistor = V × I = 3.0 × 0.02 = 60mW — a standard 1/8W (125mW) resistor is adequate.
Example 2: Finding Power Dissipation in a Shunt Resistor
A 250Ω shunt resistor is used to measure a 4-20mA current loop (converting it to 1-5V). What is the maximum power dissipated?
- Maximum current = 20mA = 0.02A
- P = I² × R = (0.02)² × 250 = 0.0004 × 250 = 0.1W (100mW)
- Use at minimum a 1/4W (250mW) resistor — ideally a 1/2W for a comfortable safety margin.
Example 3: Calculating Wire Resistance Effect
A 0-10V sensor is connected via 50m of 0.5mm² copper cable (resistance ≈ 0.034Ω/m). What is the voltage drop at 10mA signal current?
- Cable length (both ways) = 100m
- Cable resistance = 100 × 0.034 = 3.4Ω
- Voltage drop = I × R = 0.01 × 3.4 = 0.034V (34mV)
- For a 0-10V signal this is a 0.34% error — acceptable for most applications, but worth checking with thin or long cable runs.
Quick Reference: Common Voltage and Current Conversions
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| Milli | m | × 10⁻³ | 20mA = 0.020A |
| Micro | μ | × 10⁻⁶ | 100μA = 0.0001A |
| Kilo | k | × 10³ | 10kΩ = 10,000Ω |
| Mega | M | × 10⁶ | 1MΩ = 1,000,000Ω |
Important Limitations of Ohm's Law
Ohm's Law applies to ohmic (linear) components — resistors, wire, and similar passive elements. It does not directly apply to:
- Diodes and LEDs — their resistance is non-linear and varies with voltage.
- Transistors and FETs — current is controlled by a separate gate or base signal.
- Capacitors and inductors — their impedance depends on frequency (use reactance formulas: Xc = 1/2πfC and Xl = 2πfL).
- AC circuits with reactive components — use impedance (Z) instead of resistance.
Summary
Ohm's Law and the power formulas are indispensable tools. Keep this reference handy when sizing resistors, calculating power dissipation, checking voltage drops, or verifying that a circuit design is within component ratings. Once these relationships become second nature, circuit analysis becomes significantly faster and more intuitive.