NDA (II) 2016 General Ability Test · Question 74 of 150

Correct — B, 36 × 10⁵ joule. Build it from the definitions rather than from memory. A watt is one joule per second, so a kilowatt is one thousand joules every second. An hour is 3600 seconds. Energy is power multiplied by time, so one kilowatt hour is 1000 joules per second multiplied by 3600 seconds, which is 3 600 000 joules. Written in the form the options use, that is 36 × 10⁵ joule, or equivalently 3·6 × 10⁶ joule. This is the quantity your electricity supplier calls a 'unit' and bills you for, which is why the kilowatt hour survives alongside the joule — the joule is the proper SI unit but far too small for household accounting, since a single unit of electricity is three and a half million of them.

• (a)36 × 10³ joule — The right digits with the power of ten short by two. It is what you get by multiplying 3600 seconds by ten watts instead of a thousand, and it is the answer of a candidate who half-converts the kilowatt into watts.
• (c)10³ joule — This is simply the number of watts in a kilowatt, with the hour never converted at all. Power is not energy; it has to be multiplied by a time before it becomes one.
• (d)10⁵ joule — Corresponds to no step in the calculation. It is thirty-six times too small, and is offered only as a plausible-looking round number.

Power is the rate at which energy is transferred, measured in watts, where one watt is one joule per second. Energy is therefore power multiplied by time. The joule is the SI unit of energy, but for electricity supply it is inconveniently small, so the trade uses the kilowatt hour — the energy delivered by a one-kilowatt appliance running for one hour. Converting between the two needs only the fact that an hour holds 3600 seconds.

Never try to recall this figure; derive it, because the derivation takes five seconds and cannot be misremembered. Write the kilowatt as 1000 joules per second, write the hour as 3600 seconds, and multiply. The distractors in this item are all built from partial conversions, so the arithmetic itself tells you which one is right. A practical check is worth keeping too: a one-thousand-watt electric iron running for an hour consumes exactly one unit of electricity, and that is the same 3·6 million joules.

• One watt equals one joule per second, so a kilowatt is a thousand joules per second.
• One hour is 3600 seconds, so one kilowatt hour is 1000 × 3600 = 3 600 000 joules, written as 36 × 10⁵ or 3·6 × 10⁶ joule.
• The kilowatt hour is the commercial unit of electrical energy — the 'unit' shown on a domestic electricity bill.
• Energy equals power multiplied by time, which is why a power figure alone can never be an energy figure.

• Quoting a power figure when energy is asked for, or the other way round.
• Forgetting either the thousand in kilowatt or the 3600 in an hour, which is exactly how the wrong options were built.

The kilowatt hour conversion is one of the most repeated single facts in NDA GAT physics, appearing again in 2018 and 2022, so derive it once and it never has to be memorised.

• practice — not a real PYQ

  An electric heater rated at 2 kW runs for 3 hours. The energy it consumes is

  • (a)6 joule
  • (b)6 kilowatt hours
  • (c)6 watts
  • (d)6000 joules

  Answer(b) 6 kilowatt hours — energy is power multiplied by time, so 2 kW × 3 h = 6 kWh, which is 2·16 × 10⁷ joules.

• practice — not a real PYQ

  Which one of the following is a unit of power rather than of energy?

  • (a)Joule
  • (b)Kilowatt hour
  • (c)Watt
  • (d)Calorie

  Answer(c) Watt — it measures the rate of energy transfer; the other three all measure amounts of energy.