Electrical Power and Energy
Electrical power is the rate at which electrical energy is transferred or consumed in a circuit. Understanding power is essential for analyzing energy efficiency, circuit design, and electrical systems.
Definition of Electrical Power
Electrical power is the rate at which work is done or energy is transferred. It can be calculated as the product of voltage and current.
- Symbol: \(P\)
- Units: Watts (W)
- Definition: Rate of energy transfer
- Relationship: Power = Voltage × Current
Power Formulas
Power can be expressed in several equivalent forms depending on what quantities are known:
- \(P = VI\): Power equals voltage times current
- \(P = I^2R\): Power equals current squared times resistance
- \(P = \frac{V^2}{R}\): Power equals voltage squared divided by resistance
Memory Trick: Power Triangle
Remember the power formulas using the PVI triangle:
- P = Power (top of triangle)
- V = Voltage (bottom left)
- I = Current (bottom right)
To find any variable:
- P = V × I (multiply the two bottom values)
- V = P ÷ I (divide top by bottom right)
- I = P ÷ V (divide top by bottom left)
This visual triangle helps you quickly rearrange the power formula!
Energy and Power
Energy Definition
- Symbol: \(E\) or \(W\)
- Units: Joules (J)
- Relationship: \(E = Pt\)
- Definition: Total work done or energy transferred
Power vs Energy
- Power: Rate of energy transfer (watts)
- Energy: Total amount transferred (joules)
- Time factor: Energy = Power × Time
- Practical units: Kilowatt-hours (kWh) for large amounts
Power in Different Circuit Elements
Power Sources
- Batteries: Supply power to the circuit
- Generators: Convert mechanical to electrical power
- Solar panels: Convert light to electrical power
- Power supplies: Convert AC to DC power
Power Consumers
- Resistors: Convert electrical energy to heat
- Motors: Convert electrical energy to mechanical energy
- Light bulbs: Convert electrical energy to light and heat
- Electronics: Use power for various functions
Power Conservation
In any electrical circuit, power is conserved. The power supplied by sources equals the power consumed by loads.
- Power in: Sum of power from all sources
- Power out: Sum of power consumed by all loads
- Conservation: Power in = Power out
- Efficiency: Useful power output / total power input
Power Units and Conversions
Common Power Units
- Milliwatt (mW): 0.001 W
- Watt (W): 1 W
- Kilowatt (kW): 1000 W
- Megawatt (MW): 1,000,000 W
Energy Units
- Joule (J): 1 W for 1 second
- Watt-hour (Wh): 1 W for 1 hour
- Kilowatt-hour (kWh): 1000 W for 1 hour
- Practical use: kWh for electricity bills
Worked Examples
Example 1: Basic Power Calculation
Problem: A device operates at 12 V and draws 2.0 A. What is the power consumed?
Solution:
- Power formula: \(P = VI\)
- Substitution: \(P = (12 \text{ V})(2.0 \text{ A})\)
- Calculation: \(P = 24 \text{ W}\)
Answer: The power consumed is 24 W.
Example 2: Energy Calculation
Problem: A 60 W light bulb is left on for 4 hours. How much energy is consumed?
Solution:
- Energy formula: \(E = Pt\)
- Time conversion: \(t = 4 \text{ hours} = 14400 \text{ seconds}\)
- Substitution: \(E = (60 \text{ W})(14400 \text{ s})\)
- Calculation: \(E = 864000 \text{ J} = 0.24 \text{ kWh}\)
Answer: The energy consumed is 864,000 J or 0.24 kWh.
Example 3: Power from Current and Resistance
Problem: A current of 3.0 A flows through a 5.0 Ω resistor. What is the power dissipated?
Solution:
- Power formula: \(P = I^2R\)
- Substitution: \(P = (3.0)^2(5.0)\)
- Calculation: \(P = 9.0 \times 5.0 = 45 \text{ W}\)
Answer: The power dissipated is 45 W.
Interactive Power Simulation
Explore how voltage, current, and resistance affect power: