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Electric power and the kilowatt hour sheet
5-mark answer frame

Define electric power and its SI unit. Show that P = I²R and P = V²/R. Define 1 kWh, and find the cost of using a 2 kW heater for 3 hours a day for 30 days at an example rate of ₹ 7 per unit.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Define power. Electric power is the rate of using electrical energy: P = VI. SI unit: watt (W); 1 W = 1 V × 1 A.
  2. 2 · Derive the other forms.
    • Put V = IR: P = (IR) × I = I²R
    • Put I = V/R: P = V × (V/R) = V²/R
  3. 3 · Define the commercial unit. 1 kWh is the energy used by a 1 kW appliance in 1 hour. 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.
  4. 4 · Work out the bill. E = 2 kW × 3 h × 30 = 180 kWh = 180 units. Cost = 180 × ₹ 7 = ₹ 1260.
  5. 5 · Real life. We pay for energy in units, so switching off unused appliances lowers the bill.
  6. 6 · Box the answer. Energy used = 180 kWh; cost = ₹ 1260 at the example rate.

Scoring tip: Change watts to kilowatts and minutes to hours before you multiply. 1 unit = 1 kWh.