Ch 31: Alternating Current

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 31: Alternating Current

Problem 34a

Chapter 31, Problem 34a

Off to Europe! You plan to take your hair dryer to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The dryer puts out 1600 W at 120 V. What could you do to operate your dryer via the 240 V line in Europe?

Verified step by step guidance

Understand the relationship between power, voltage, and resistance. The power (P) of an electrical device is given by the formula:

P = V^{2} / R

, where V is the voltage and R is the resistance.

Calculate the resistance of the hair dryer when it operates at 120 V. Use the formula:

R = V^{2} / P

. Substitute V = 120 V and P = 1600 W to find R.

Determine the current (I) that the hair dryer draws at 120 V using the formula:

I = P / V

. Substitute P = 1600 W and V = 120 V to find I.

To operate the dryer at 240 V, you need to ensure that the power remains the same (1600 W). Use the formula:

P = V × I

to find the new current I at 240 V.

Consider using a step-down transformer or a voltage converter to reduce the 240 V supply to 120 V, allowing the dryer to operate safely without exceeding its designed power rating.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Voltage

Voltage, measured in volts (V), is the potential difference between two points in an electrical circuit. It drives the flow of electric current, similar to how pressure drives water through pipes. In this scenario, understanding the difference between the 120 V in the US and the 240 V in Europe is crucial for adapting the hair dryer to operate safely and effectively.

Power

Power, measured in watts (W), is the rate at which electrical energy is consumed or converted into other forms of energy. The hair dryer operates at 1600 W, which is the product of voltage and current (P = VI). Knowing the power rating helps determine how the dryer will function under different voltages and what adjustments are necessary to maintain its performance.

Electrical Resistance

Electrical resistance, measured in ohms (Ω), is the opposition to the flow of electric current. It is related to voltage and current by Ohm's Law (V = IR). When using the dryer in Europe, understanding how resistance affects current flow at different voltages is essential for ensuring the device operates within safe limits and does not overheat or get damaged.

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Textbook Question

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

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Textbook Question

A series ac circuit contains a 250-Ω resistor, a 15-mH inductor, a 3.5-μF capacitor, and an ac power source of voltage amplitude 45 V operating at an angular frequency of 360 rad/s.What is the power factor of this circuit?

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Textbook Question

An L-R-C series circuit with L = 0.120 H, R = 240 Ω, and C = 7.30 μF carries an rms current of 0.450 A with a frequency of 400 Hz. What are the phase angle and power factor for this circuit?

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Textbook Question

An L-R-C series circuit is connected to a 120-Hz ac source that has V_rms = 80.0 V. The circuit has a resistance of 75.0 Ω and an impedance at this frequency of 105 Ω. What average power is delivered to the circuit by the source?

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Textbook Question

A Step-Down Transformer. A transformer connected to a 120 V (rms) ac line is to supply 12.0 V (rms) to a portable electronic device. The load resistance in the secondary is 5.00 Ω. What should the ratio of primary to secondary turns of the transformer be?

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