The cost of energy to operate an industrial refrigerator that consumes 5 kW power working 10 hours per day for 30 days will be (Given that the charge per kWh of energy = ₹ 4)
- (a)₹ 600
- (b)₹ 6,000
- (c)₹ 1,200
- (d)₹ 1,500
Correct — B, Rs 6,000. Energy used = power x time = 5 kW x 10 hours x 30 days = 1,500 kWh (units). At Rs 4 per kWh, the cost = 1,500 x Rs 4 = Rs 6,000. The trick is to convert the whole running period into kilowatt-hours first, then multiply by the tariff.
- (a)Rs 600 — This is 150 kWh x Rs 4. You get 150 kWh by multiplying 5 kW x 30 days but forgetting the 10 hours of running each day.
- (c)Rs 1,200 — This equals 300 kWh x Rs 4 and undercounts the total energy by a factor of five; the correct running total is 1,500 kWh, not 300.
- (d)Rs 1,500 — This is the number of units (1,500 kWh) written as if it were the cost in rupees; it forgets to multiply by the Rs 4 per-unit tariff (it effectively assumes Rs 1 per unit).
Electrical energy is measured in kilowatt-hours (kWh). Power in kilowatts multiplied by the running time in hours gives the energy in kWh, and one kWh is the 'unit' that electricity boards bill. The cost is simply the total energy in units multiplied by the tariff per unit.
Work in two steps. First convert everything into kilowatt-hours over the full period (power x hours per day x number of days), then multiply by the per-unit charge. The wrong options each drop one factor - the hours, the days, or the tariff.
- One commercial 'unit' of electricity equals one kilowatt-hour (1 kWh = 1000 watt-hours).
- Energy (kWh) = power (kW) x time (hours); here 5 x 10 x 30 = 1,500 kWh.
- One kilowatt-hour equals 3.6 x 10^6 joules (3.6 megajoules).
- Cost = total units x tariff = 1,500 kWh x Rs 4 = Rs 6,000.
- Confusing power (kW), which is a rate, with energy (kWh), which is power multiplied by time.
- Forgetting to multiply by BOTH the hours per day and the number of days.
- Forgetting the final step of multiplying units by the per-unit tariff.
NDA sets a numerical 'find the electricity bill' item: convert power and running time into kWh, then multiply by the tariff.
No directly related past PYQ was found.
- practice — not a real PYQ
A 100 W bulb is used for 10 hours a day. How much electrical energy does it consume in 30 days?
- (a)30 kWh
- (b)3 kWh
- (c)300 kWh
- (d)0.3 kWh
Answer(a) 30 kWh - 0.1 kW x 10 h x 30 days = 30 kWh.
- practice — not a real PYQ
One 'unit' of electrical energy shown on a domestic electricity bill is equal to
- (a)1 watt
- (b)1 joule
- (c)1 kilowatt-hour
- (d)1 kilowatt
Answer(c) 1 kilowatt-hour - the standard billing unit of electrical energy.