NDA (II) 2022 General Ability Test · Question 61 of 150

Correct — A, 3·6 × 10⁶ J. One kilowatt-hour is the energy consumed by a device drawing one kilowatt of power for one hour. Energy equals power multiplied by time, so 1 kWh = 1000 W × 3600 s. A watt is one joule per second, so the product is 1000 × 3600 = 3,600,000 joules, or 3·6 × 10⁶ J. This is the quantity billed as one unit of electricity on a domestic meter; the joule itself is far too small to bill in, which is why the commercial unit is the kilowatt-hour.

• (b)3·6 × 10³ J — 3,600 joules is one watt-hour, not one kilowatt-hour. This comes from converting the hour to 3600 seconds but forgetting the factor of 1000 in the prefix kilo.
• (c)10³ J — This is just the numerical value of the prefix kilo and ignores the hour entirely. A kilowatt is a rate of energy use, and it becomes an amount of energy only when multiplied by a time.
• (d)1 J — The joule is the SI unit of energy itself. One kilowatt-hour is 3.6 million times larger than a joule, which is precisely why electricity bills are not written in joules.

Power is the rate at which energy is used and is measured in watts, where one watt is one joule per second. Energy is the total amount used and is the product of power and time. For household and industrial billing, the joule is inconveniently small, so the practical unit is the kilowatt-hour — the energy drawn by a one-kilowatt load running for one hour. On a domestic electricity bill this is what is called one unit.

The item is two conversions and nothing more. The prefix kilo contributes a factor of 10³ and the hour contributes 3600 seconds, which is 3·6 × 10³, so 1 kWh = 10³ × 3·6 × 10³ = 3·6 × 10⁶ J. Each wrong option is built from doing only one of the two conversions, or neither. The habit worth building is to keep power and energy strictly apart — a watt or kilowatt is a rate, a joule or kilowatt-hour is an amount, and a bill charges for the amount.

• One watt is one joule per second, so energy equals power multiplied by time.
• 1 kilowatt-hour = 1000 W × 3600 s = 3·6 × 10⁶ J.
• One kilowatt-hour is what is called one unit of electricity on a domestic bill.
• 3,600 J is one watt-hour; a kilowatt-hour is a thousand times larger than that.

• Applying only one of the two conversions, so that kilo is dropped or the hour is not turned into 3600 seconds.
• Treating the kilowatt as a unit of energy; it is a unit of power.

Either a direct unit conversion as here, or a numerical item that asks for units consumed and the resulting bill from an appliance rating.

• practice — not a real PYQ

  An electric heater rated 2 kW is used for 3 hours every day. The energy it consumes in 30 days is

  • (a)60 kWh
  • (b)90 kWh
  • (c)180 kWh
  • (d)360 kWh

  Answer(c) 180 kWh — energy = 2 kW × 3 h × 30 days.

• practice — not a real PYQ

  Which one of the following is NOT a unit of energy?

  • (a)joule
  • (b)kilowatt-hour
  • (c)electron-volt
  • (d)watt

  Answer(d) watt — the watt is a unit of power, that is, energy per unit time.