An 80 W fan, a 60 W bulb and a 500 W washing machine are operated for 15, 20 and 1 hr, respectively. The total electrical power units consumed are
Understand the Problem
The question requires calculating the total electrical power consumed by three devices (a fan, a bulb, and a washing machine) based on their power ratings and the time they are operated. To solve this, we will find the energy consumed by each device in kilowatt-hours and then sum them up.
Answer
The total electrical power units consumed are \( 2.9 \, \text{kWh} \).
Answer for screen readers
The total electrical power units consumed are ( 2.9 , \text{kWh} ).
Steps to Solve
- Convert Power Ratings to Kilowatts
First, convert the power ratings of the devices from watts to kilowatts.
- Fan: $80 \text{ W} = 0.08 \text{ kW}$
- Bulb: $60 \text{ W} = 0.06 \text{ kW}$
- Washing Machine: $500 \text{ W} = 0.5 \text{ kW}$
- Calculate Energy Consumed by Each Device
Next, calculate the energy consumed (in kilowatt-hours) by each device using the formula:
$$ \text{Energy} = \text{Power (kW)} \times \text{Time (hr)} $$
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Energy consumed by the fan: $$ E_{\text{fan}} = 0.08 , \text{kW} \times 15 , \text{hr} = 1.2 , \text{kWh} $$
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Energy consumed by the bulb: $$ E_{\text{bulb}} = 0.06 , \text{kW} \times 20 , \text{hr} = 1.2 , \text{kWh} $$
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Energy consumed by the washing machine: $$ E_{\text{washing machine}} = 0.5 , \text{kW} \times 1 , \text{hr} = 0.5 , \text{kWh} $$
- Sum Up the Energy Consumption
Now, sum the energy consumed by all devices to find the total energy consumption:
$$ E_{\text{total}} = E_{\text{fan}} + E_{\text{bulb}} + E_{\text{washing machine}} $$
Substituting the values we calculated:
$$ E_{\text{total}} = 1.2 , \text{kWh} + 1.2 , \text{kWh} + 0.5 , \text{kWh} = 2.9 , \text{kWh} $$
The total electrical power units consumed are ( 2.9 , \text{kWh} ).
More Information
The calculations show that the total energy consumed by the three devices is 2.9 kilowatt-hours, which can help in understanding energy usage and costs.
Tips
- Forgetting to convert watts to kilowatts: Always ensure power ratings are in kilowatts when calculating energy consumption.
- Miscalculating time: Double-check the time values given in the problem to avoid errors in the final energy calculations.
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