A family uses 5 CFLs of 10W each for 10 hours every day, 5 fans of 100 W each for 15 hours every day, an air conditioner of 2kW for 10 hours every day, a washing machine of 1kW for 3 hours every week. Calculate the amount of electrical energy in kWh consumed by the family in a year.

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Solution

Step 1: Given
For CFL,
$P o w e r, P_{1} = 10 W T i m e, t_{1} = 10 h o u r s / d a y N o . o f C F L s, n_{1} = 5$
For fans,
$P o w e r, P_{2} = 100 W T i m e, t_{2} = 15 h o u r s N o . o f f a n s, n_{2} = 5$
For the air conditioner,
$P o w e r, P_{3} = 2 k W T i m e, t_{3} = 10 h o u r s / d a y N o . o f A C s, n_{3} = 1$
For the washing machine,
$P o w e r, P_{4} = 1 k W T i m e, t_{4} = 3 h o u r s / w e e k N o . o f w a s h in g m a c h i n e s, n_{4} = 1$
Step 2: Total energy consumption by CFLs
Let the energy consumption by CFLs in a year be $E_{1}$ .
$E_{1} = P_{1} \times t_{1} \times n_{1} \times 365 = 10 W \times 10 h o u r s / d a y \times 5 \times 365 d a y s = 10 \times 10 \times 5 \times 365 = 182500 W h = 182.5 k W h$
Step 3: Total energy consumption by fans
Let the energy consumption by fans in a year be $E_{2}$ .
$E_{2} = P_{2} \times t_{2} \times n_{2} \times 365 = 100 W \times 15 h o u r s / d a y \times 5 \times 365 d a y s = 100 \times 15 \times 5 \times 365 = 2737500 W h = 2737.5 k W h$
Step 4: Total energy consumption by air conditioners
Let the energy consumption by air conditioners in a year be $E_{3}$ .
$E_{3} = P_{3} \times t_{3} \times n_{3} \times 365 = 2000 W \times 10 h o u r s / d a y \times 1 \times 365 d a y s = 2000 \times 10 \times 1 \times 365 = 7300000 W h = 7300 k W h$
Step 5: Total energy consumption by washing machine
Let the energy consumption by washing machine in a year be $E_{4}$ .
$E_{4} = P_{4} \times t_{4} \times n_{4} \times 52 = 1000 W \times 3 h o u r s / w e e k \times 1 \times 52 w e e k s = 1000 \times 3 \times 1 \times 52 = 156000 W h = 156 k W h$
Step 6: Total energy consumption by the family in a year
Let the total energy consumption by the family in a year be $E$ .
$E = E_{1} + E_{2} + E_{3} + E_{4} = 182.5 k W h + 2737.5 k W h + 7300 k W h + 156 k W h = 10376 k W h$
Hence, the total energy consumption by the family in a year is 10376 kWh.

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