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Chapter 22: Problem 36

a. What is the resistance of a \(1500 \mathrm{W}\) ( \(120 \mathrm{V}\) ) hair dryer? b. What is the current in the hair dryer when it is used?

Short Answer

Expert verified
The resistance of a \(1500 \mathrm{W}\) ( \(120 \mathrm{V}\) ) hair dryer is \(9.6 \Omega\), and the current when it is used is \(12.5 \mathrm{A}\).

Step by step solution

01

Calculate the Resistance

The first part of the problem asks for the resistance of a \(1500 \mathrm{W}\) (\(120 \mathrm{V}\)) hair dryer. We know that Power (P) = Voltage (V) * Current (I). Rearranging this equation, we get Current (I) = Power (P) / Voltage (V). Substituting the given values for P and V, we get: I = \(1500 \mathrm{W}\) / \(120 \mathrm{V}\) = \(12.5 \mathrm{A}\).\n \nNext, using Ohm's law (V = IR), we can find the resistance. Rearranging the formula, we get Resistance (R) = Voltage (V) / Current (I). Substituting our calculated current and the given voltage in this formula, we get: R = \(120 \mathrm{V}\) / \(12.5 \mathrm{A}\) = \(9.6 \Omega\).
02

Calculate the Current

The second part of the problem asks for the current in the hair dryer when it is used. However, we have already calculated this in step 1 while finding the resistance. Therefore, the current in the dryer when it is used is \(12.5 \mathrm{A}\).

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Key Concepts

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

Power Formula
The power formula is a critical concept in the realm of electronics and electrical engineering. Power, stated in watts (W), is the rate at which electrical energy is consumed or converted into another form of energy. In mathematical terms, the power in an electrical circuit can be calculated by the product of voltage and current: \( P = VI \).

The power formula allows us to determine the energy usage of devices. For example, the power consumption of a hair dryer can be derived by multiplying the voltage by the current it draws. This relationship can be rearranged to solve for other variables, such as resistance or current, if power and one other variable are known. In practical terms, this formula helps determine a device's electrical efficiency and energy cost over its operation.

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Most popular questions from this chapter

In Example 22.6 the length of a \(60 \mathrm{W}, 240 \Omega\) lightbulb filament was calculated to be \(60 \mathrm{cm}\). a. If the potential difference across the filament is \(120 \mathrm{V},\) what is the strength of the electric field inside the filament? b. Suppose the length of the bulb's filament were doubled without changing its diameter or the potential difference across it. What would the electric field strength be in this case? c. Remembering that the current in the filament is proportional to the electric field, what is the current in the filament following the doubling of its length? d. What is the resistance of the filament following the doubling of its length?

When running on its \(11.4 \mathrm{V}\) battery, a laptop computer uses \(8.3 \mathrm{W} .\) The computer can run on battery power for \(9.0 \mathrm{h}\) before the battery is depleted. a. What is the current delivered by the battery to the computer? b. How much energy, in joules, is this battery capable of supplying? c. How high off the ground could a \(75 \mathrm{kg}\) person be raised using the energy from this battery?

Variations in the resistivity of blood can give valuable clues to changes in the blood's viscosity and other properties. The resistivity is measured by applying a small potential difference and measuring the current. Suppose a medical device attaches electrodes into a \(1.5-\mathrm{mm}-\) diameter vein at two points \(5.0 \mathrm{cm}\) apart. What is the blood resistivity if a \(9.0 \mathrm{V}\) potential difference causes a \(230 \mu\) A current through the blood in the vein?

A \(60-\mathrm{cm}-\) long heating wire is connected to a \(120 \mathrm{V}\) outlet. If the wire dissipates \(45 \mathrm{W},\) what are (a) the current in and (b) the resistance of the wire?

A wire with resistance \(R\) is connected to the terminals of a \(6.0 \mathrm{V}\) battery. What is the potential difference \(\Delta V_{\text {ends }}\) between the ends of the wire and the current \(I\) through it if the wire has the following resistances? (a) \(1.0 \Omega\) (b) \(2.0 \Omega\) (c) \(3.0 \Omega.\)
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