/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 19 Off to Europe! You plan to take ... [FREE SOLUTION] | 91Ó°ÊÓ

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

Short Answer

Expert verified
Use a step-down transformer. The current is 13.33 A; resistance is 9 Ω.

Step by step solution

01

Understand the Problem

Your hair dryer is designed for the US voltage of 120 V but will be used in Europe where outlets provide 240 V. Therefore, we need to determine what modifications, if any, are needed to operate the dryer safely. Additionally, we need to find out the current and resistance when the dryer operates at 240 V.
02

Determine Necessary Modifications

Since the power rating of the dryer is given as 1600 W at 120 V, using just a plug adapter won't work because the dryer would receive too much power. You would need a step-down transformer that converts 240 V to 120 V so the dryer receives the power it is rated for.
03

Calculate Current at 120 V

First, find the current the dryer draws in the US by using the formula for power: \[ P = IV \] where \(P\) is power, \(I\) is current, and \(V\) is voltage. Rearranging gives:\[ I = \frac{P}{V} = \frac{1600 \, \text{W}}{120 \, \text{V}} = 13.33 \, \text{A} \]
04

Calculate Current at 240 V with Step-down Transformer

The dryer is still expected to draw the same current of 13.33 A since the step-down transformer converts 240 V to 120 V.
05

Calculate Resistance at 120 V

To find the resistance when operating at 120 V, use Ohm’s law: \[ V = IR \Rightarrow R = \frac{V}{I} = \frac{120 \, \text{V}}{13.33 \, \text{A}} \approx 9 \Omega \]
06

Calculate Resistance at 240 V

Since we know both the current and the voltage the dryer would expect, the resistance remains constant. Therefore, the resistance will still be approximately 9 Ω, as resistance does not change with voltage unless the material or configuration changes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Voltage Conversion
When traveling to a different country, like Europe, it's essential to understand that the voltage level can differ from what your appliances are designed for. Voltage conversion helps ensure that devices operate optimally without causing damage.

For example, if an appliance is designed to run on 120 V, but you're in a country where the standard is 240 V, such as many in Europe, adjustments are needed. In this case, you'll need a step-down transformer. This device reduces the 240 V supply to 120 V, which is what the appliance expects. Without this conversion, the appliance could receive too much power, risk overheating, or even cause hazards.

It's a straightforward but crucial aspect when using electrical devices in different regions. Always make sure these adjustments are in place when planning to use electrical gadgets abroad, to avoid any unintended mishaps.
Ohm's Law
Ohm's Law forms the basis for understanding how voltage, current, and resistance relate in electrical circuits. It's one of the fundamental principles in electrical engineering. The law is succinctly expressed with the equation: \[ V = IR \] where:
  • \( V \) represents voltage
  • \( I \) represents current
  • \( R \) represents resistance


This relationship shows that the current through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant. When you know two of the values, you can easily find the third.

For example, if you know your device's operating voltage and current, you can calculate its resistance. This understanding is particularly useful when working with appliances across different power systems and ensures that you can adjust and use devices safely.
Power Calculation
Power calculation is a critical aspect of ensuring that electrical devices function correctly and safely. In essence, power is the rate at which electrical energy is consumed by an appliance, expressed in watts (W). The formula is:\[ P = IV \]where:
  • \( P \) is the power in watts
  • \( I \) is the current in amperes
  • \( V \) is the voltage in volts


For instance, in the US, an appliance like a hair dryer designed for 120 V could have a power output of 1600 W. Calculating power helps us identify how much current the device will need at different voltages. It’s crucial not to confuse the power rating under different voltages, directly affecting how much power and energy the appliance consumes.

If a step-down transformer is involved, as is often needed when adjusting to a new voltage, this calculation becomes vital to ensure the appliance is safely operable under new conditions.
Resistance Measurement
Resistance measurement tells us how much a component or appliance opposes the flow of electric current. Using Ohm’s Law, resistance (R) can be found if the current (I) and voltage (V) across the device are known: \[ R = \frac{V}{I} \]Resistance is measured in ohms (Ω).

In practical terms, knowing a device's resistance helps determine if it can safely handle the expected voltage and current without risk of overheating or malfunctioning. An appliance's resistance doesn’t change unless its material properties or design configuration changes.

For electrical appliances, once the resistance at specific voltage and current is known, this value remains constant even if the operating voltage changes. This concept simplifies predicting an appliance's behavior under different electrical conditions, ensuring optimal and safe performance when switching between different electrical systems.

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Most popular questions from this chapter

An LCR series circuit with \(100 \Omega\) resistance is connected to an \(A C\) source of \(200 V\) and angular frequency 300 radians/sec. When only the capacitance is removed The current lags behind the voltage by \(60^{\circ} .\) When only the inductance is removed the current leads the voltage \(60^{\circ}\). Calculate the current and the power dissipated in the LCR circuit.

An \(L-R-C\) series circuit is connected to a \(120-\mathrm{Hz}\) ac source that has \(V_{\mathrm{rms}}=80.0 \mathrm{~V}\). The circuit has a resistance of \(75.0 \Omega\) and an impedance at this frequency of \(105 \Omega\). What average power is delivered to the circuit by the source?

You want to double the resonance angular frequency of an \(L-R-C\) series circuit by changing only the pertinent circuit elements all by the same factor. (a) Which ones should you change? (b) By what factor should you change them?

A resistance \(R\), capacitance \(C\), and inductance \(L\) are connected in series to a voltage source with amplitude \(V\) and variable angular frequency \(\omega .\) If \(\omega=\omega_{0}\), the resonance angular frequency, find (a) the maximum current in the resistor; (b) the maximum voltage across the capacitor; (c) the maximum voltage across the inductor; (d) the maximum energy stored in the capacitor; (e) the maximum energy stored in the inductor. Give your answers in terms of \(R, C, L\), and \(V\).

In an \(L-R-C\) series circuit, the source has a voltage amplitude of \(120 \mathrm{~V}, R=80.0 \Omega\), and the reactance of the capacitor is \(480 \Omega .\) The voltage amplitude across the capacitor is \(360 \mathrm{~V}\). (a) What is the current amplitude in the circuit? (b) What is the impedance? (c) What two values can the reactance of the inductor have? (d) For which of the two values found in part (c) is the angular frequency less than the resonance angular frequency? Explain.

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