CDS (I) 2023 General Knowledge · Question 8 of 120

Correct — A, 3.00. A unit of electrical energy is one kilowatt-hour, the energy used by a one-kilowatt appliance running for one hour, so the working has to be done in kilowatts and hours. The bulb is 100 watts, which is 0.1 kilowatt. In one day it runs for 10 hours, so it uses 0.1 multiplied by 10, that is 1 kilowatt-hour, or exactly one unit a day. Over 3 days that is 3 units. Written out, energy equals power multiplied by time equals 0.1 kW times 10 h times 3 days, which is 3.00 kWh.

• (b)1.08 — A number that appears if the working drifts into joules and back — a kilowatt-hour is 3.6 million joules, and mixing that conversion into a calculation already done in kilowatts and hours corrupts the answer. Keep the units the question supplies.
• (c)2.16 — Twice the previous distractor, and produced the same way. If a step involves 3.6 anywhere while power is already in kilowatts and time in hours, the conversion has been applied twice.
• (d)0.33 — The reciprocal of the right answer, obtained by dividing where the formula multiplies. Energy grows with both power and time, so three days of use cannot come to less than one day of it.

Electrical energy is power multiplied by time. The SI unit, the joule, is inconveniently small for a household bill, so electricity is sold in kilowatt-hours: one kilowatt drawn for one hour, which works out to 3.6 million joules. On a bill this is simply called a unit. Any consumption sum therefore has the same three steps — put the power in kilowatts, put the time in hours, multiply.

The arithmetic here is trivial and the marks are really for unit discipline, which is why every wrong option is a unit accident rather than a factual error. Convert 100 watts to 0.1 kilowatt at the start and the rest is mental arithmetic. A useful benchmark to carry out of this question: a 100-watt lamp burning ten hours a day costs exactly one unit a day, so an old-style bulb left on all evening is measurably more expensive than the LED that has replaced it, an LED of similar brightness drawing under a tenth of the power.

• One unit of electrical energy is one kilowatt-hour, equal to 3.6 x 10^6 joules.
• Energy consumed equals power in kilowatts multiplied by time in hours.
• A 100-watt appliance is a 0.1-kilowatt appliance, so ten hours of use is exactly one unit.
• The watt is the SI unit of power, one joule per second, and is named after James Watt.

• Leaving the power in watts and reporting an answer thousands of times too large.
• Multiplying by 3.6 x 10^6 in a sum that is already in kilowatt-hours.
• Forgetting to multiply the daily figure by the number of days.

As a units-consumed sum like this one, as a cost sum with a rupees-per-unit rate attached, or as a straight conversion of one kilowatt-hour into joules.

• practice — not a real PYQ

  An electric heater rated 2 kW is used for 5 hours a day. The number of units of electrical energy it consumes in a day is

  • (a)2
  • (b)5
  • (c)10
  • (d)25

  Answer(c) 10 — energy equals power times time, 2 kW multiplied by 5 h, which is 10 kWh or 10 units.

• practice — not a real PYQ

  One kilowatt-hour of electrical energy is equal to

  • (a)3.6 x 10^3 J
  • (b)3.6 x 10^5 J
  • (c)3.6 x 10^6 J
  • (d)3.6 x 10^9 J

  Answer(c) 3.6 x 10^6 J — one kilowatt is 1000 joules per second, and an hour is 3600 seconds.