Problem 25 - Physics

Question

In doing a load of clothes, a clothes dryer uses \(16 \mathrm{~A}\) of current at \(240 \mathrm{~V}\) for \(45 \mathrm{~min}\). A personal computer, in contrast, uses \(2.7\) A of current at \(120 \mathrm{~V}\). With the energy used by the clothes dryer, how long (in hours) could you use this computer to "surf" the Internet?

Step-by-Step Solution

Answer

You can use the computer for approximately 8.89 hours.

Step 1: Calculate Energy Used by the Dryer

First, we need to calculate the energy used by the clothes dryer. The formula to calculate energy in kilowatt-hours (kWh) is \( \text{Energy} = \text{Power} \times \text{Time} \). Power \( P \) in watts is given by \( P = IV \), where \( I \) is the current in amperes and \( V \) is the voltage. For the dryer: \[ P = 16 \text{ A} \times 240 \text{ V} = 3840 \text{ W} \]Convert minutes to hours for the energy calculation:\[ 45 \text{ min} = 0.75 \text{ hours} \]The energy used by the dryer in kWh is:\[ \text{Energy} = 3840 \text{ W} \times 0.75 \text{ hours} = 2880 \text{ watt-hours} = 2.88 \text{ kWh} \]

Step 2: Calculate Power Used by the Computer

Now, calculate the power used by the personal computer. Again, use the formula \( P = IV \).For the computer:\[ P = 2.7 \text{ A} \times 120 \text{ V} = 324 \text{ W} \]

Step 3: Determine Usage Time for Computer

With the energy measurement from the dryer, calculate how long the computer can run. The formula for time when energy and power are known is \( \text{Time} = \frac{\text{Energy}}{\text{Power}} \).\[ \text{Time} = \frac{2.88 \text{ kWh}}{324 \text{ W}} = \frac{2880 \text{ Wh}}{324 \text{ W}} \approx 8.89 \text{ hours} \]

Step 4: Convert and Round the Final Result

The computer can be used for approximately \(8.89\) hours with the energy equivalent to what the dryer uses. Since it is common to round time to the nearest hundredth for practical scenarios, the result remains 8.89 hours.

Key Concepts

Power Calculation

Power is a measure of how quickly work is done or energy is transferred. It is calculated using the formula \( P = IV \), where \( P \) represents power in watts, \( I \) is the current in amperes, and \( V \) is the voltage in volts.
For example, if a device uses a current of 10 amperes at 120 volts, the power consumed can be calculated by plugging in the values: \( P = 10 ext{ A} \times 120 ext{ V} = 1200 ext{ W} \). This means the device consumes 1200 watts of power.

• Power is essential for determining how much energy a device uses over time.
• The higher the power, the more energy is consumed in a given period.

Current and Voltage

Current and voltage are fundamental concepts in electrical circuits. Current measures the flow of electric charge and is expressed in amperes (A). Voltage, on the other hand, is the potential difference that drives the flow of electric charge, measured in volts (V).
Understanding the relationship between current and voltage is crucial, as they directly impact a device's power consumption. As seen in the formula \( P = IV \):

• If current or voltage increases, the power of the device also increases.
• It is important to ensure devices operate within their specified current and voltage ratings to avoid damage.

Electrical Energy

Electrical energy is the energy consumed or used by electrical devices. It is typically measured in watt-hours (Wh) or kilowatt-hours (kWh).
To calculate energy, you multiply the power by the time the device is in use: \( ext{Energy} = ext{Power} \times ext{Time} \).
Suppose a device operates at 100 watts for 2 hours. The energy consumed is \( 100 ext{ W} \times 2 ext{ hrs} = 200 ext{ Wh} \).

• Proper calculation helps in understanding the cost and efficiency of using electrical devices.
• Electrical energy is often a consideration in energy conservation efforts and sustainability practices.

Kilowatt-hour

A kilowatt-hour (kWh) is a unit of energy that represents the consumption of 1,000 watts over the period of one hour. This is a standard unit of measurement used by utility companies to charge for electricity usage.
Imagine using a 1,000-watt heater for one hour. It consumes 1 kWh of energy.

• Converting to kWh makes it more manageable to express larger quantities of energy.
• Understanding kWh is vital for both estimating electricity costs and comparing the energy efficiency of different appliances.