BPSC 71st CCE Prelims General Studies · Question 123 of 150

Correct — C, 9×10⁸. The whole question rests on knowing what a 'unit' means on an electricity bill. One unit is the Board of Trade unit, which is one kilowatt-hour: the energy delivered when a load of one kilowatt runs for one hour. Convert it to SI step by step and nothing is left to memory — one kilowatt is 1,000 watts, one watt is one joule per second, and one hour is 3,600 seconds, so 1 kWh = 1,000 J/s × 3,600 s = 3,600,000 J = 3.6 × 10⁶ J. A month's consumption of 250 units is therefore 250 × 3.6 × 10⁶ = 900 × 10⁶ = 9 × 10⁸ joules, which is option (c). The Commission printed this same working in the remarks it published on 31 October 2025 while disposing of candidate objections, setting out the energy consumed as 250 kWh and equating it to 9 × 10⁸ J. Two habits make this a ten-second question rather than a thirty-second one. First, fix 3.6 × 10⁶ J per unit in memory as a single number, the way you would fix 4.186 J per calorie; every domestic-electricity numerical in every state PSC paper reduces to multiplying by it. Second, do the arithmetic in powers of ten and let the exponent do the checking: 250 is 2.5 × 10², so 2.5 × 3.6 = 9 and 10² × 10⁶ = 10⁸, giving 9 × 10⁸ with no long multiplication at all. Note also what the question is really testing, because it is not arithmetic. It is the distinction between power and energy — the kilowatt is a rate of using energy while the kilowatt-hour is a quantity of energy, and the electricity board bills you for the second, never the first. A candidate who half-remembers the conversion as 3,600 J, which is the value for one watt-hour rather than one kilowatt-hour, lands squarely on option (a); the factor of a thousand between the watt and the kilowatt is the only thing separating the two answers on this paper. For a feel for the size of the number, 9 × 10⁸ J is the energy a single 100-watt bulb would consume if it burned continuously for 2,500 hours, that is for more than a hundred days without a break — which is precisely why the joule is useless for billing and the kilowatt-hour exists.

• (a)9×10⁵ — The most reasoned wrong answer on the list, and the one the option set was built to catch. It is 250 × 3,600, the figure you get by treating one unit as one WATT-hour (3.6 × 10³ J) instead of one KILOWATT-hour (3.6 × 10⁶ J) — a slip of exactly a factor of a thousand. In real terms 9 × 10⁵ J is a quarter of a single unit, less than what one ceiling fan draws in a night, so it cannot be a household's monthly bill.
• (b)8×10⁶ — No standard slip in the conversion produces this figure; it sits on the list as a magnitude decoy between the two derivable values, so that a candidate who guesses by 'feel' rather than converting cannot land on the answer. Checked against the meter it is absurd: 8 × 10⁶ J divided by 3.6 × 10⁶ J per unit is about 2.2 units, that is under one per cent of the 250 units the stem states.
• (d)10⁵ — Smaller still, and the easiest to eliminate on sight. 10⁵ J is 0.028 kWh — about one thirty-sixth of a single unit, or the energy a 100-watt bulb uses in roughly seventeen minutes. Candidates reach it by treating the '250 units' as though the unit were already a joule-scale quantity. Any answer that makes a month of household electricity smaller than one billed unit has failed the reality check before the arithmetic begins.

Energy and power are different physical quantities and the exam tests the boundary between them relentlessly. Energy is the capacity to do work; its SI unit is the joule, defined as the work done when a force of one newton moves its point of application through one metre, and named after James Prescott Joule (1818-1889), whose paddle-wheel experiments established the mechanical equivalent of heat. Power is the RATE at which energy is transferred, measured in watts, where one watt is one joule per second. Rearranged, energy = power × time, and that single rearrangement generates the kilowatt-hour: a kilowatt of load running for an hour delivers 1,000 × 3,600 = 3.6 × 10⁶ joules. Electricity utilities bill in kilowatt-hours, called 'units' on Indian bills, for the practical reason that the joule is far too small a parcel to be convenient — a household month written in joules runs to nine hundred million of them. The same logic produces the whole family of energy units the exam uses: the calorie (4.186 J) for food and heat, the erg (10⁻⁷ J) in the older CGS system, the electronvolt (1.602 × 10⁻¹⁹ J) for atomic and nuclear physics, and, at national scale, the billion unit or BU (10⁹ kWh, equal to 3.6 × 10¹⁵ J) in which India's annual electricity generation is reported. Every one of them is a joule with a different number of zeroes attached, chosen so that the numbers people actually quote stay between one and a thousand.

Reason to the answer in three moves. First, translate the word 'unit': on an Indian electricity bill one unit is one kilowatt-hour, nothing else. Second, build the conversion rather than recalling it, so that you cannot misremember it — kilowatt means 1,000 joules per second, an hour means 3,600 seconds, and the product is 3.6 × 10⁶ J. Third, multiply: 250 × 3.6 × 10⁶ = 9 × 10⁸ J. The single discriminating fact is the KILO in kilowatt-hour. Options (c) and (a) differ by exactly one thousand, which is exactly the factor between a watt-hour and a kilowatt-hour, so the entire question turns on whether you carried that prefix. Everything else on the option list — 8 × 10⁶ and 10⁵ — is orders of magnitude too small and can be struck out by a sanity check before any multiplication: a household consuming 250 units cannot possibly have used less energy than two or three of them. That reality check is the transferable skill here. Convert the candidate answer back into units and see whether it describes a month of living or a few minutes of a light bulb. There is one further habit worth building for this whole block of the paper. Do exponent arithmetic separately from digit arithmetic: 250 = 2.5 × 10², and 2.5 × 3.6 = 9 exactly, while 10² × 10⁶ = 10⁸. The clean digit 9 falling out is itself a signal that the intended route has been taken, because examiners choose data that produce round answers.

• One 'unit' on an Indian electricity bill is one kilowatt-hour, historically the Board of Trade unit: 1 kWh = 1,000 W × 3,600 s = 3.6 × 10⁶ J. Hence 250 units = 250 × 3.6 × 10⁶ = 9 × 10⁸ J, the working the Commission itself set out in its remarks published on 31 October 2025.
• The joule is the SI unit of energy and work — the work done when a force of one newton acts through one metre — named after James Prescott Joule (1818-1889), who established the mechanical equivalent of heat. The watt is one joule per second, so energy equals power multiplied by time.
• Other energy units the exam uses, all reducible to joules: 1 calorie = 4.186 J, 1 kilocalorie (the dietary Calorie) = 4,186 J, 1 erg = 10⁻⁷ J in the CGS system, and 1 electronvolt = 1.602 × 10⁻¹⁹ J in atomic and nuclear physics.
• A 100-watt bulb burning for 10 hours consumes exactly 1 kWh, that is one billed unit or 3.6 × 10⁶ J — the quickest mental anchor for converting appliance ratings into units, and the reason the same bulb running non-stop would need about 2,500 hours to account for the 9 × 10⁸ J in this question.
• At national scale India reports electricity generation in billion units (BU), where 1 BU = 10⁹ kWh = 3.6 × 10¹⁵ J, and installed capacity in megawatts and gigawatts — capacity is a power figure while generation is an energy figure, and confusing the two is the standard trap in economy questions on the power sector.
• The prefix, not the formula, is where this item is set to be lost: one watt-hour is 3,600 J while one kilowatt-hour is 3,600,000 J, a factor of exactly 1,000, which is the entire distance between option (a) and the correct option (c) on this paper.

• Converting one unit as 3,600 J instead of 3,600,000 J — that is a watt-hour, not a kilowatt-hour, and it drops the answer by a factor of a thousand straight onto option (a)
• Treating the kilowatt and the kilowatt-hour as interchangeable: the kilowatt is a rate of consuming energy and the kilowatt-hour is a quantity of it, which is why capacity is quoted in MW but generation in kWh
• Skipping the reality check — any answer that makes a month of household electricity equal to a few minutes of one light bulb should be struck out before the arithmetic is even attempted

BPSC keeps unit conversion as a bare one-step numerical with the options separated only by powers of ten, so the mark is decided by whether you carried the prefix rather than by any physics; the Commission even published the multiplication in its remarks. UPSC almost never asks the conversion directly — it asked units in 1999 as a matching list pairing Mach, angstrom, pascal and joule with speed, wavelength, pressure and energy, and it tests the kilowatt-hour indirectly in economy questions, as in 2008 when it asked whether India's annual generation of about 660 billion kWh was correctly stated alongside installed capacity in megawatts.

• practice — not a real PYQ

  An electric heater rated 2 kilowatts is used for 5 hours a day. The energy consumed in 30 days, in units (kWh), is

  • (a)30 units
  • (b)60 units
  • (c)150 units
  • (d)300 units

  Answer(d) 300 units — energy = power × time = 2 kW × 5 h = 10 kWh per day, and 10 × 30 = 300 kWh, that is 300 units, equal to 1.08 × 10⁹ J.

• practice — not a real PYQ

  Which one of the following is a unit of energy and not of power ?

  • (a)Watt
  • (b)Kilowatt
  • (c)Kilowatt-hour
  • (d)Horsepower

  Answer(c) Kilowatt-hour — it is power multiplied by time and therefore a quantity of energy, equal to 3.6 × 10⁶ J. The watt, the kilowatt and the horsepower are all rates of energy transfer, that is units of power.