Electric power and energy

Electric power is how fast electrical energy is used:

P = V I = I² R = V² / R

measured in watts (W): 1 W = 1 volt × 1 ampere. A kilowatt (kW) is 1000 W. A 220 V bulb drawing 0.50 A uses 220 × 0.50 = 110 W.

Which form to use? Pick the one with the quantity that stays the same. Bulbs on the mains all get the same 220 V, so use P = V²/R: a 60 W bulb has more resistance than a 100 W bulb. When the same bulb is put on a different voltage, its resistance stays the same, so again use P = V²/R.

Example: a 220 V, 100 W bulb on 110 V. Its resistance R = 220²/100 stays the same. At 110 V, P = 110²/R = 100 × (110/220)² = 25 W. Half the voltage gives a quarter of the power, not half.

Energy = power × time. Electricity companies measure it in kilowatt hours (kW h): the 'unit' on your electricity bill.

1 kW h = 1000 W × 3600 s = 3.6 × 10⁶ J

Keep power in kW and time in hours.

Example from the book: a 400 W refrigerator runs 8 hours a day for 30 days.

• Power = 400 W = 0.4 kW.
• Time = 8 × 30 = 240 h.
• Energy = 0.4 × 240 = 96 kW h.
• At ₹3.00 per kW h, the cost is 96 × 3 = ₹288.

"Are electrons used up in a circuit?" No. They just flow round and round. When we pay the electricity bill, we pay for the energy used to push them through the fans, lights and other appliances, not for the electrons.