Which one of the following is the value of 1 kWh of energy converted into joules ?
- (a)1·8 × 10⁶ J
- (b)3·6 × 10⁶ J
- (c)6·0 × 10⁶ J
- (d)7·2 × 10⁶ J
Correct — B, 3·6 × 10⁶ J. Energy equals power multiplied by time, so a kilowatt-hour is simply one kilowatt sustained for one hour. Convert each part to base units. One kilowatt is one thousand watts, and a watt is one joule per second. One hour is sixty minutes of sixty seconds each, which is three thousand six hundred seconds. Multiplying, one thousand joules per second times three thousand six hundred seconds gives three million six hundred thousand joules, written 3·6 × 10⁶ J.
- (a)1·8 × 10⁶ J — This is exactly half the right value, the figure you get for half a kilowatt-hour or for one kilowatt run for thirty minutes. It usually appears when 1800 is used for the number of seconds in an hour.
- (c)6·0 × 10⁶ J — This comes from multiplying a thousand watts by six thousand, and there is no quantity in the problem equal to six thousand seconds. An hour has 3600 seconds, not 6000.
- (d)7·2 × 10⁶ J — This is twice the correct answer, the energy in two kilowatt-hours. It follows from using 7200 seconds, which is two hours rather than one.
The joule is the SI unit of energy, and the watt is the SI unit of power, equal to one joule per second. Because the joule is inconveniently small for household use, electricity is billed in kilowatt-hours, also called Board of Trade units. One kilowatt-hour is the energy consumed by a one-kilowatt appliance running for one hour, and equals 3·6 million joules. That single conversion factor, 3·6 × 10⁶, is the one number worth memorising from this chapter.
Every wrong option here is generated by mishandling the seconds in an hour, so the safest method is to convert the units one at a time and never to guess the factor whole. Write the kilowatt as 10 cubed watts, write the hour as 3600 seconds, and multiply. It also helps to have the practical picture attached to the number — a one-kilowatt electric iron running for one hour, or a hundred-watt bulb burning for ten hours, each consume exactly one unit on the household meter. Watch out for a favourite examiner trick of printing the same value in an unfamiliar dress, such as 36 × 10⁵ joule, which is the very same quantity written with the decimal point moved.
- One watt is one joule per second, and one kilowatt is one thousand watts.
- One hour is 3600 seconds, so one kilowatt-hour is 3·6 × 10⁶ joules.
- The kilowatt-hour is the commercial unit of electrical energy, the 'unit' on a household bill.
- A 100 W bulb burning for 10 hours consumes exactly one kilowatt-hour.
- The watt-hour and the newton-metre are units of energy; the kilogram-metre per second squared is a unit of force.
- Using the wrong number of seconds in an hour, which produces every one of the wrong options here.
- Confusing the kilowatt, a unit of power, with the kilowatt-hour, a unit of energy.
- Failing to recognise the same value written as 36 × 10⁵ instead of 3·6 × 10⁶.
Asked as a straight conversion, as a bill calculation from an appliance rating and running hours, or as an odd-one-out among units of energy.
One kilowatt hour is equal to
- (a) 36 × 10³ joule
- (b) 36 × 10⁵ joule
- (c) 10³ joule
- (d) 10⁵ joule
Answer(b) 36 × 10⁵ joule
The identical conversion set eighteen months earlier, and a useful warning that the same value can be dressed up as 36 × 10⁵ instead of 3·6 × 10⁶.
The commercial unit of electrical energy is kilowatt-hour (kWh), which is equal to
- (a) 3·6 × 10⁶ J
- (b) 3·6 × 10³ J
- (c) 10³ J
- (d) 1 J
Answer(a) 3·6 × 10⁶ J
The same number asked a third time, four years later, which is about as clear a signal as NDA gives that this conversion is worth memorising.
- practice — not a real PYQ
An electric heater rated 2 kW runs for 3 hours a day. The energy it consumes in a day is
- (a)2 kWh
- (b)3 kWh
- (c)6 kWh
- (d)12 kWh
Answer(c) 6 kWh — energy equals power times time, so 2 kW multiplied by 3 hours.
- practice — not a real PYQ
Which one of the following is NOT a unit of energy?
- (a)Joule
- (b)Watt-hour
- (c)Newton-metre
- (d)Watt
Answer(d) Watt — the watt measures power, which is energy per unit time, not energy itself.