Power

• The definition of power and its units (Watt and kilowatt-hour)
• Why appliances have power ratings and how they draw current
• The connection between power, fuses, and circuit safety
• How to calculate electricity bills using kWh

What is power? Power is the rate at which work is done, or the rate at which energy is transferred:

P = W / t

where:

• P = power (Watts, W)
• W = work done or energy transferred (Joules, J)
• t = time (seconds, s)

1 Watt = 1 Joule per second. A 60 W light bulb converts 60 J of electrical energy to light and heat every second.

Power can also be written in terms of force and velocity:

P = F × v

This form is useful when a force moves an object at a constant speed (e.g., a car engine producing 50 kN of thrust at 30 m/s produces 50000 × 30 = 1,500,000 W = 1.5 MW of power).

Units of power

• Watt (W): SI unit, 1 W = 1 J/s
• Kilowatt (kW): 1 kW = 1000 W (used for appliances and engines)
• Megawatt (MW): 1 MW = 10⁶ W (used for power plants)
• Horsepower (hp): 1 hp ≈ 746 W (older unit, still common for motors/engines)

Unit of electrical energy: kilowatt-hour (kWh) The commercial (electricity billing) unit of energy is the kilowatt-hour:

1 kWh = 1 kW × 1 hour = 1000 J/s × 3600 s = 3.6 × 10⁶ J = 3.6 MJ

Electricity meters record consumption in kWh. This is the unit on your electricity bill.

Appliance power ratings and current draw Every electrical appliance has a power rating. In India, mains voltage is 230 V. The current drawn by an appliance is:

I = P / V

Examples:

• Electric kettle (2000 W): I = 2000/230 ≈ 8.7 A
• Ceiling fan (75 W): I = 75/230 ≈ 0.33 A
• AC unit (1500 W): I = 1500/230 ≈ 6.5 A

Why the fuse blows A fuse is a safety device — a thin wire that melts if current exceeds its rated value (typically 5 A or 15 A for household circuits). When you switch on a kettle (8.7 A) and a fan (0.33 A) together, the total current is about 9 A — manageable. But adding an AC unit (6.5 A more) could push total current above the fuse rating (e.g., 15 A), causing it to blow. The fuse melts deliberately to prevent the wiring from overheating and causing a fire.

Power and energy distinction Power = rate of energy transfer (W = J/s). Energy = amount transferred over time (J or kWh). A 2000 W kettle running for 3 minutes uses:

Energy = P × t = 2000 W × (3 × 60 s) = 360,000 J = 0.1 kWh

That 0.1 kWh is what appears on your electricity bill (multiplied by the rate per kWh).

Problem: A 100 W light bulb is kept on for 10 hours every day for 30 days. Electricity costs ₹6 per kWh. (a) What is the total energy consumed in kWh? (b) What is the total cost?

Solution:

(a) Energy consumed per day: E_day = P × t = 100 W × 10 h = 1000 Wh = 1 kWh

Energy in 30 days: E_total = 1 kWh/day × 30 days = 30 kWh

(b) Cost: Cost = 30 kWh × ₹6/kWh = ₹180

So keeping a single 100 W bulb on for 10 hours a day for a month costs ₹180. Replacing it with a 10 W LED that produces similar brightness would reduce this cost to ₹18 — a saving of ₹162 per month per bulb.

• Confusing power (W) with energy (J or kWh). Power is the rate; energy is the total. An appliance rated at 1000 W doesn't mean it stores 1000 J — it means it uses 1000 J every second it runs.
• Forgetting to convert time to seconds when calculating energy in Joules. E = Pt requires t in seconds when P is in Watts and E is in Joules.
• Assuming all appliances on the same circuit add their wattages for fuse calculation. Correct — total current = sum of individual currents = sum of (P/V) for each appliance. Exceeding fuse rating causes it to blow.
• Treating kWh as a unit of power. The kWh is energy (power × time). 1 kWh ≈ 3.6 MJ.

1. A 500 W motor lifts a load for 20 seconds. How much work does it do (in Joules)?
2. A 1500 W geyser runs for 2 hours daily for 30 days. Find the energy consumed in kWh and the cost at ₹5/kWh.
3. Two appliances rated 800 W and 1200 W are connected on a 230 V circuit with a 10 A fuse. Will the fuse blow?