Power and Its Unit
📚 Key Concepts of Power
🔹 Real-Life Example
Two people climb the same stairs, but one takes 30 seconds while the other takes 60 seconds. Both do the same work, but the faster person has twice the power.
A 100W light bulb consumes 100 joules of energy every second. A car engine rated at 150 horsepower can do work faster than a 100-horsepower engine.
Power: The rate at which work is done or energy is transferred.
🧪 Important Formulas
🔸 Power Formula
P = W / t
Where:
- P = Power (W)
- W = Work done (J)
- t = Time taken (s)
🔸 Alternative Forms
- P = F × v (when force and velocity are in the same direction)
- P = E / t (rate of energy transfer)
🔹 Units of Power
- SI Unit: Watt (W) = J/s
- Larger Units:
- Kilowatt (kW) = 1000 W
- Megawatt (MW) = 10⁶ W
- Horsepower (hp) = 746 W
🔍 Advanced: Commercial Unit of Energy
1 kWh = 3.6 × 10⁶ J
This is the unit used in electricity bills:
- 1 kWh = Energy consumed by 1 kW appliance in 1 hour
- Cost calculation: Units consumed × Rate per unit
🔹 Power in Daily Life
- Light bulbs: 5W LED, 60W incandescent
- Appliances: 1500W microwave, 2000W hair dryer
- Vehicles: 150 hp car engine
- Power plants: 1000 MW nuclear plant
Problem: If 300 J of work is done in 10 seconds, calculate the power.
Problem : A car accelerates from rest to 20 m/s in 5 seconds. If the car’s mass is 1200 kg, calculate the net force acting on the car. Tests understanding of Newton’s second law and kinematics by finding acceleration first, then applying F = ma.
Problem : An electric heater consumes 2000 W of power and operates for 3 hours. Calculate the total electrical energy consumed in kilowatt-hours (kWh). Tests the relationship between power, energy, and time using the formula Energy = Power × Time with unit conversion.