DC Circuits · #2 of 48

Ohm's Law + Power

V = I × R, P = V × I

Why it matters

Ohm’s Law is the foundation of all electronics. Without it, you’re guessing. Power tells you if components will overheat and fail.

The idea

Ohm’s Law

The relationship between voltage (V), current (I), and resistance (R): V = I × R

flowchart LR
    V[Voltage V] -->|Ohm's Law| I[Current I]
    R[Resistance R] -->|Ohm's Law| I
    V -->|Power| P[Power P]
    I -->|Power| P

What It Means

Voltage (V): The “pressure” pushing electrons
Current (I): The flow of electrons (amps)
Resistance (R): How much the circuit “resists” current (ohms)

Power

Power is energy per unit time: P = V × I

Power becomes heat
Components have maximum power ratings
Exceed the rating → component fails (sometimes spectacularly)

Real-World Example

ESP32 GPIO pin at 3.3V driving an LED with 220Ω resistor:

I = V / R = 3.3V / 220Ω = 15mA
P_resistor = I² × R = (0.015A)² × 220Ω = 0.05W (safe, resistors are usually 0.25W+)
P_LED = V_LED × I = ~2V × 15mA = 0.03W (check LED datasheet)

Demo

Adjust Voltage and Resistance to see how current and power change.

Watch for:

High current → components heat up (red indicator)
Safe operating zone → green indicator
Power limit → what happens if you exceed component ratings

I: 3.30 mA P: 10.9 mW

voltage: 3.3 V resistance: 1000 Ω

Key takeaways

V = I × R — know any two, calculate the third
P = V × I — power becomes heat
Components have maximum power ratings — exceed them at your peril
Always calculate current before connecting components

Going deeper

Ohm’s Law applies to linear (resistive) circuits. Diodes, transistors, and other non-linear components have more complex relationships. For DC circuits with resistors, Ohm’s Law is king.

Math details

Ohm's Law:
  V = I × R
  I = V / R
  R = V / I

Power:
  P = V × I
  P = I² × R  (substitute V = I×R)
  P = V² / R  (substitute I = V/R)

Example calculations:
  Given: V = 5V, R = 1000Ω
  I = 5V / 1000Ω = 0.005A = 5mA
  P = 5V × 0.005A = 0.025W = 25mW

Component ratings:
  Resistor: usually 0.25W (1/4W) or 0.5W (1/2W)
  LED: typically 20mA max current, ~0.1W power
  ESP32 GPIO: 40mA max source, 28mA max sink

Implementation

LLM Prompt: Current Calculator

Write a Rust function that calculates current and power given voltage and resistance.
Include safety checks: warn if current exceeds 40mA (ESP32 GPIO limit) or
if power exceeds 0.25W (common resistor rating). Return Result with error messages.

Lab Exercise

Measure a 220Ω resistor with multimeter (should read ~220Ω)
Connect LED + 220Ω resistor to 3.3V power supply
Measure voltage across resistor (should be ~1.3V if LED drops 2V)
Calculate current: I = V_resistor / R = 1.3V / 220Ω ≈ 5.9mA
Verify LED is bright but not dim (if dim, resistor is too large)

⚡ Ohm's Law + Power