Problem 39 - College Physics

Question

Off to Europe! You plan to take your hair blower to Europe, where the electrical outlets put out 240 \(\mathrm{V}\) instead of the 120 \(\mathrm{V}\) seen in the United States. The blower puts out 1600 \(\mathrm{W}\) at 120 \(\mathrm{V}\) . (a) What could you do to operate your blower via the 240 \(\mathrm{V}\) line in Europe? (b) What current will your blower draw from a European outlet? (c) What resistance will your blower appear to have when operated at 240 \(\mathrm{V} ?\)

Step-by-Step Solution

Answer

Use a voltage converter to operate the blower. The blower draws 6.67 A at 240 V, and its resistance is 36 ohms.

Step 1: Determine Power Appliance Requires

The hair blower operates at 1600 Watts (W) with a voltage of 120 Volts (V). The power required by the appliance does not change with voltage, so the blower still requires 1600 Watts even at a different voltage.

Step 2: Calculate Current at 120 Volts

Using the power formula \( P = IV \), where \( P \) is power, \( I \) is current, and \( V \) is voltage, we first find the current drawn at 120 V:\[ I = \frac{P}{V} = \frac{1600}{120} = 13.33 \text{ A} \]

Step 3: Use Transformer or Converter

To operate the blower on a 240 V outlet, use a step-down transformer or voltage converter that adjusts the voltage from 240 V to 120 V. This way, the blower will operate under its designed specifications.

Step 4: Calculate Current at 240 Volts

If operated directly at 240 V, the power formula is still relevant. Given the power requirement is constant at 1600 W, apply \( I = \frac{P}{V} \):\[ I = \frac{1600}{240} = 6.67 \text{ A} \]

Step 5: Calculate Resistance at 240 Volts

Assuming the blower is made to operate directly at 240 V, use the formula \( P = V^2/R \) to determine resistance \( R \). Re-arrange to \( R = \frac{V^2}{P} \):\[ R = \frac{240^2}{1600} = 36 \text{ ohms} \]

Key Concepts

Voltage Conversion

When traveling to different regions, you might encounter different voltage standards. For instance, the United States typically uses 120 volts (V) outlets, while many European countries use 240 volts. This variation requires a voltage conversion to safely use devices across these regions.

To operate your hair blower in Europe without damage, you need a tool like a step-down transformer or voltage converter. These devices alter the voltage from 240 V to the 120 V that your blower is designed for.

Here's how it works:

• The transformer adjusts the voltage level without altering the power needed by your appliance.
• It's important to match the converter with the wattage of your device to ensure smooth operation.

By using the correct converter, your appliances remain efficient and safe, avoiding potential over-voltage damage.

Power Calculation

Power calculation is crucial for understanding how much energy your appliance consumes. Here, the hair blower uses 1600 watts (W) when functioning at 120 V. But what happens to this power usage across different voltages? Good question!

Power, measured in watts, is the product of the current (measured in amperes, A) and voltage (measured in volts, V). It's represented by the formula \( P = I \times V \).

• Power remains constant as voltage changes because the appliance requires the same amount of energy to function properly.
• This constancy is key when adapting devices to new power sources such as different electrical outlets.

Hence, whether at 120 V in the US or 240 V in Europe, the blower still demands 1600 W ensuring consistent performance.

Electric Current

Electric current indicates how much charge is flowing through a circuit, measured in amperes (A). To find out the current your blower draws in different settings, you can rearrange the power formula: \( I = \frac{P}{V} \).

When your blower is in the US, plugged into a 120 V outlet, it draws:

• \( I = \frac{1600}{120} = 13.33 \) A

In Europe, at 240 V, it pulls less current because of the increased voltage:

• \( I = \frac{1600}{240} = 6.67 \) A

Understanding these dynamics helps in anticipating how appliances function under different electrical systems, ensuring you’re prepared to handle your devices smoothly wherever you go.

Resistance Calculation

Resistance, measured in ohms (Ω), regulates how much current flows for a given voltage, following Ohm's law: \( V = I^{-1}R \). To find the resistance when using a higher voltage like 240 V, we can start from the power equation: \( P = \frac{V^2}{R} \).

Rearranging gives \( R = \frac{V^2}{P} \). Plug in the values for your blower:

• \( R = \frac{240^2}{1600} = 36 \) Ω

This means, operating at 240 V, the device shows a resistance of 36 ohms.

Knowing the resistance aids in understanding how effortlessly current can move through the circuit when connected to different voltages. It’s an essential part of predicting how your device adapts across regions, maintaining its functionality and your safety.