/*! 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 36 A toaster is rated at \(600 \mat... [FREE SOLUTION] | 91Ó°ÊÓ

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A toaster is rated at \(600 \mathrm{W}\) when connected to a \(120-\mathrm{V}\) source. What current does the toaster carry, and what is its resistance?

Short Answer

Expert verified
The toaster carries a current of 5 Amperes and has a resistance of 24 Ohms.

Step by step solution

01

Determination of Current

The power \(P\) of an electrical appliance can be expressed as \(P=IV\) where \(I\) is the current and \(V\) the voltage. We can rearrange this formula to find the current, \(I = P/V\). Substitute \(P = 600W\) and \(V = 120V\) into the formula to find the current.
02

Calculation of Current

Substitute the given values into the formula \(I = P/V\). So, \(I = 600W/120V = 5A\). The toaster carries 5 Amperes.
03

Determination of Resistance

The resistance \(R\) of a toaster can be found using Ohm's law \(V = IR\) where \(V\) is the voltage, \(I\) is the current and \(R\) is the resistance. We can rearrange this formula to find the resistance, \(R = V/I\). Substitute \(V=120V\) and \(I=5A\) into the formula to find the resistance.
04

Calculation of Resistance

Substitute the given values into the formula \(R = V/I\). So, \(R = 120V/5A = 24Ω\). The resistance of the toaster is 24 Ohms.

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Key Concepts

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

Understanding Electrical Power
Electrical power is an essential concept in the world of electronics. It is the measure of how much energy is used or produced by an electrical device and is often described in watts (W). In our everyday examples, like a toaster, electrical power tells us how much electrical energy it uses to generate heat to toast your bread. The general formula for electrical power is given by:\[P = I \times V\]where:
  • \(P\) is the power in watts.
  • \(I\) is the current in amperes.
  • \(V\) is the voltage in volts.
This formula shows that electrical power is the product of the current flowing through a device and the voltage supplied across it. This relationship helps us understand how devices use energy in electrical circuits. When we know the voltage and the power rating of a device, we can easily find the current it uses with simple calculations.
Knowing the power helps manufacturers rate appliances like toasters, giving you a clear idea of their energy consumption.
Current Calculation Simplified
Current is the flow of electric charge in a circuit and is measured in amperes (A). Calculating current is essential because it tells us how much electricity is flowing through a device like your toaster. We use the formula of power to calculate current:\[I = \frac{P}{V}\]This simple rearrangement of the power formula allows us to calculate current when power and voltage are known. From our exercise, the toaster has a power rating of \(600 \text{ W}\) when connected to a \(120 \text{ V}\) supply.
Substituting these values, we get:\[I = \frac{600 \text{ W}}{120 \text{ V}} = 5 \text{ A}\]So, the toaster carries a current of \(5\) amperes. Knowing the current helps ensure that we use the right wires and protect the circuits, as too much current can lead to overheating or even electrical fires.
Resistance Determination Explained
Resistance measures how much a component, like the toaster, opposes the flow of electric current. It is measured in ohms (\(Ω\)). The concept of resistance is fundamental in designing and operating all electrical devices safely and efficiently.According to Ohm’s Law, we can calculate the resistance using the formula:\[R = \frac{V}{I}\]Where:
  • \(R\) is the resistance in ohms.
  • \(V\) is the voltage in volts.
  • \(I\) is the current in amperes.
With the values from the exercise, the voltage is \(120 \text{ V}\) and the current is \(5 \text{ A}\). Substituting these values, we find:\[R = \frac{120 \text{ V}}{5 \text{ A}} = 24 \text{ Ω}\]The toaster hence has a resistance of \(24\) ohms. Understanding resistance is vital because it determines how much current flows through a circuit for a given voltage. It helps in controlling and managing the energy usage of devices.

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Most popular questions from this chapter

An electric car is designed to run off a bank of \(12.0-\mathrm{V}\) batteries with total energy storage of \(2.00 \times 10^{7} \mathrm{J} .\) (a) If the electric motor draws \(8.00 \mathrm{kW},\) what is the current delivered to the motor? (b) If the electric motor draws \(8.00 \mathrm{kW}\) as the car moves at a steady speed of \(20.0 \mathrm{m} / \mathrm{s}\), how far will the car travel before it is "out of juice"?

An \(11.0-\) W energy-efficient fluorescent lamp is designed to produce the same illumination as a conventional \(40.0-\mathrm{W}\) incandescent lightbulb. How much money does the user of the energy-efficient lamp save during 100 hours of use? Assume a cost of \(\$ 0.080\) 0/kWh for energy from the power company.

Compute the cost per day of operating a lamp that draws a current of \(1.70 \mathrm{A}\) from a \(110-\mathrm{V}\) line. Assume the cost of energy from the power company is \(\$ 0.0600 / \mathrm{kWh}\).

A \(10.0-\mathrm{V}\) battery is connected to a \(120-\Omega\) resistor. Ignoring the internal resistance of the battery, calculate the power delivered to the resistor.

The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius \(1.00 \mathrm{mm} .\) (a) The beam current is \(8.00 \mu \mathrm{A}\). Find the current density in the beam, assuming that it is uniform throughout. (b) The specd of the clectrons is so close to the speed of light that their specd can be taken as \(c=3.00 \times 10^{8} \mathrm{m} / \mathrm{s}\) with negligible error. Find the clectron density in the beam. (c) How long does it take for Avogadro's number of electrons to emerge from the accelerator?

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