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Power and Energy

Understanding electrical power consumption and energy storage

Electrical Power

Power is the rate at which electrical energy is transferred or converted. It measures how much energy is used per unit time.

Power Formula:

P = V × I

where:

  • P = Power (Watts, W)
  • V = Voltage (Volts, V)
  • I = Current (Amperes, A)

Alternative Power Formulas:

P = I² × R (using Ohm's Law)

P = V² / R (using Ohm's Law)

All three formulas are equivalent and derived from P = V × I and V = I × R

Electrical Energy

Energy is the total amount of work done by electricity over time. It's measured in Joules (J) or kilowatt-hours (kWh) for practical applications.

Energy Formula:

E = P × t

where:

  • E = Energy (Joules, J or Watt-seconds)
  • P = Power (Watts, W)
  • t = Time (seconds, s)

Practical Energy Units:

  • 1 Joule (J) = 1 Watt × 1 second
  • 1 kilowatt-hour (kWh) = 1000 W × 3600 s = 3.6 MJ
  • Your electricity bill is measured in kWh

Worked Examples

Example 1: LED Power

A red LED runs at 2V with 20mA current. Calculate the power:

P = V × I = 2V × 0.02A = 0.04W = 40mW

Example 2: Resistor Power

A 220Ω resistor with 10mA current. Find power dissipation:

P = I² × R = (0.01A)² × 220Ω = 0.022W = 22mW

Example 3: Energy Consumption

A 60W light bulb runs for 5 hours. Calculate energy used:

E = P × t = 60W × 5h = 300Wh = 0.3kWh

At $0.12/kWh, this costs: 0.3 × $0.12 = $0.036 (about 4 cents)

Power Ratings and Safety

Every component has a maximum power rating. Exceeding this causes overheating and component failure.

Common Power Ratings:

  • Resistors: 1/8W, 1/4W, 1/2W, 1W
  • LEDs: 20-30mW typical
  • Small transistors: 500mW-1W
  • Power transistors: 10W-100W+

Safety Rule: Always ensure components operate well below their maximum power rating (typically 50-70% max) to prevent overheating and extend component life.