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Explain why kilowatt hour is a unit of energy not power.

Physics

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2 parts
a

R0.45\text{R0.45}

b

R0.53\text{R0.53}

Step-by-step solution

8 steps

Here are the solutions to your questions:

  1. Explain why kilowatt hour is a unit of energy not power.

    A kilowatt hour (kWh\text{kWh}) is a unit of energy because it represents the product of power (kilowatt) and time (hour). Energy is defined as the capacity to do work, and it is calculated by multiplying the rate at which work is done (power) by the duration over which it is done (time). Power, on the other hand, is the rate of energy transfer or consumption, measured in watts or kilowatts.

  2. In the following questions, use a tariff of R1.50\text{R1.50} per kilowatt hour (including VAT).

Part a· 4 steps

Four 15 W15\, \text{W} energy saving bulbs are switched on for 5 hours5\, \text{hours} in the evening. Calculate cost (R\text{R}).

  1. Calculate the total power of the bulbs.

    $$
    \text{Total Power} = 4\, \text{bulbs} \times 15\, \text{W/bulb} = 60\, \text{W}
    $$
    
  2. Convert the total power from watts to kilowatts.

    $$
    \text{Total Power} = 60\, \text{W} \times \frac{1\, \text{kW}}{1000\, \text{W}} = 0.060\, \text{kW}
    $$
    
  3. Calculate the total energy consumed in kilowatt hours.

    $$
    \text{Energy} = \text{Power} \times \text{Time}
    $$
    $$
    \text{Energy} = 0.060\, \text{kW} \times 5\, \text{hours} = 0.30\, \text{kWh}
    $$
    
  4. Calculate the total cost.

    $$
    \text{Cost} = \text{Energy} \times \text{Tariff}
    $$
    $$
    \text{Cost} = 0.30\, \text{kWh} \times \text{R1.50/kWh} = \text{R}0.45
    $$
    The cost is $\boxed{\text{R0.45}}$.
    

Part b

R0.53\text{R0.53}

Calculate the cost of using a 100 W100\, \text{W} heater for 3 hours3\, \text{hours} and 30 min30\, \text{min}.

  1. Convert the power from watts to kilowatts.

    $$
    \text{Power} = 100\, \text{W} \times \frac{1\, \text{kW}}{1000\, \text{W}} = 0.100\, \text{kW}
    $$
    
  2. Convert the total time to hours.

    $$
    \text{Time} = 3\, \text{hours} + 30\, \text{min} \times \frac{1\, \text{hour}}{60\, \text{min}}
    $$
    $$
    \text{Time} = 3\, \text{hours} + 0.5\, \text{hours} = 3.5\, \text{hours}
    $$
    
  3. Calculate the total energy consumed in kilowatt hours.

    $$
    \text{Energy} = \text{Power} \times \text{Time}
    $$
    $$
    \text{Energy} = 0.100\, \text{kW} \times 3.5\, \text{hours} = 0.35\, \text{kWh}
    $$
    
  4. Calculate the total cost.

    $$
    \text{Cost} = \text{Energy} \times \text{Tariff}
    $$
    $$
    \text{Cost} = 0.35\, \text{kWh} \times \text{R1.50/kWh} = \text{R}0.525
    $$
    The cost is $\boxed{\text{R0.53}}$.
    
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