/*! 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 57 An \(18.0 \mathrm{~W}\) device h... [FREE SOLUTION] | 91Ó°ÊÓ

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An \(18.0 \mathrm{~W}\) device has \(9.00 \mathrm{~V}\) across it. How much charge goes through the device in \(4.00 \mathrm{~h}\) ?

Short Answer

Expert verified
28800 C of charge goes through the device in 4 hours.

Step by step solution

01

Understand the Relationship

The power \((P)\) of a device can be calculated using the formula \(P = VI\), where \(V\) is the voltage and \(I\) is the current. We need to find \(I\) first to use it subsequently in our calculations.
02

Calculate Current

We know that the power \(P\) is 18.0 W and the voltage \(V\) is 9.00 V. Using the formula \(P = VI\), rearrange for current \(I\): \[ I = \frac{P}{V} = \frac{18.0}{9.00} = 2.00 \text{ A} \]
03

Calculate the Total Charge

To find the total charge \(Q\) that passes through the device, use the formula \(Q = It\), where \(t\) is the time in seconds. Convert 4.00 hours to seconds: \(4.00 \times 3600 = 14400\) seconds. Then calculate: \[ Q = 2.00 \times 14400 = 28800 \text{ C} \]
04

Conclude Your Answer

The total charge that goes through the device in 4 hours is 28800 C.

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Key Concepts

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

Electrical Power
Electrical power is a fundamental concept that describes the rate at which electrical energy is transferred by an electric circuit. It is measured in watts \(\text{W}\), and is given by the product of voltage and current in a circuit. This relationship can be expressed by the equation \(P = VI\), where \(P\) is the power, \(V\) is the voltage, and \(I\) is the current.
To put this into perspective, consider a simple electrical device that requires energy to operate. The power rating of this device tells you how much energy it consumes over time. For example, if you have an 18-watt device operating on a 9-volt power supply, you'll need to multiply these numbers to understand the electrical power relationship.
  • Power is measured in watts \(\text{(W)}\).
  • It's the product of current (in amperes \(\text{(A)}\)) and voltage (in volts \(\text{(V)}\)).
  • The formula is expressed as \(P = VI\).
Electric Current
Electric current is the flow of electric charge through a conductor, such as a wire. It is measured in amperes (A). Imagine it as a stream of water flowing through a pipe, where the water represents the electric charge. The amount of charge passing through each point of the circuit per second is the electric current.
To calculate the current when the power and voltage are known, you can rearrange the formula for electrical power to solve for current: \(I = \frac{P}{V}\).When working with electrical systems, understanding the current is crucial because it helps us design efficient and safe systems. A higher current means more charge is flowing, which could heat the wire excessively if it's not designed to handle that flow. In our exercise, we found that with the given power and voltage, the current is 2.00 A.
  • Current is the rate of flow of electric charge.
  • Measured in amperes \(\text{(A)}\).
  • Determined by dividing power by voltage: \(I = \frac{P}{V}\).
Voltage
Voltage, often referred to as electric potential difference, is the work needed per unit charge to move a test charge between two points in an electric field. It is measured in volts \(\text{(V)}\). Think of it as the 'pressure' that pushes the electric charge through a circuit.
The voltage in a circuit helps to determine how much energy per charge is available to be converted into other forms of energy, like light or heat, as the charges are pushed through the circuit.In relation to our exercise, understanding voltage is essential to predicting how much "push" the electric charges have as they pass through the device. With 9 volts, we are ensuring the appropriate level of electrical "pressure" is applied to maintain an efficient operation of the 18-watt device.
  • Voltage is the potential difference between two points in an electric field.
  • It constitutes the driving force behind the movement of electrons.
  • The unit of voltage is volts \(\text{(V)}\).

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Most popular questions from this chapter

An isolated conducting sphere has a \(10 \mathrm{~cm}\) radius. One wire carries a current of \(1.0000020\) A into it. Another wire carries a current of \(1.0000000\) A out of it. How long would it take for the sphere to increase in potential by \(1000 \mathrm{~V} ?\)

A human being can be electrocuted if a current as small as \(50 \mathrm{~mA}\) passes near the heart. An electrician working with sweaty hands makes good contact with the two conductors he is holding, one in each hand. If his resistance is \(2000 \Omega\), what might the fatal voltage be?

A certain \(x\) -ray tube operates at a current of \(7.00 \mathrm{~mA}\) and \(\mathrm{a}\) potential difference of \(80.0 \mathrm{kV}\). What is its power in watts?

A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to \(440 \mathrm{~A} / \mathrm{cm}^{2} .\) What diameter of cylindrical wire should be used to make a fuse that will limit the current to \(0.50 \mathrm{~A}\) ?

A Nichrome heater dissipates \(500 \mathrm{~W}\) when the applied potential difference is \(110 \mathrm{~V}\) and the wire temperature is \(800^{\circ} \mathrm{C}\). What would be the dissipation rate if the wire temperature were held at \(200^{\circ} \mathrm{C}\) by immersing the wire in a bath of cooling oil? The applied potential difference remains the same, and \(\alpha\) for Nichrome at \(800^{\circ} \mathrm{C}\) is \(4.0 \times 10^{-4} \mathrm{~K}^{-1}\).

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