/*! 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 38 A battery-powered global positio... [FREE SOLUTION] | 91Ó°ÊÓ

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A battery-powered global positioning system (GPS) receiver operating on 9.0 V draws a current of 0.13 A. How much electrical energy does it consume during 30 minutes?

Short Answer

Expert verified
2106 joules.

Step by step solution

01

Understand Key Concepts

Electrical energy consumed can be calculated using the formula \(E = V \times I \times t\), where \(E\) is energy in joules, \(V\) is voltage in volts, \(I\) is current in amperes, and \(t\) is time in seconds.
02

Convert Units

Convert the time from minutes to seconds since the formula requires time in seconds. 30 minutes is equivalent to \(30 \times 60 = 1800\) seconds.
03

Substitute Values into Formula

Substitute \(V = 9.0\) volts, \(I = 0.13\) amperes, and \(t = 1800\) seconds into the formula \(E = V \times I \times t\).
04

Calculate Electrical Energy

Calculate \[ E = 9.0 \text{ V} \times 0.13 \text{ A} \times 1800 \text{ s} = 2106 \text{ J} \].
05

Conclusion

The GPS receiver consumes 2106 joules of electrical energy during 30 minutes.

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Key Concepts

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

Electrical energy
Electrical energy is the energy that is generated or used when electrical currents flow through a circuit. This energy is essential for powering everyday devices, like the GPS receiver mentioned in the exercise. Electrical energy is often measured in joules (J). It can be calculated using the formula:\[ E = V \times I \times t \]where:
  • \(E\) is the electrical energy in joules,
  • \(V\) is the voltage in volts,
  • \(I\) is the current in amperes,
  • \(t\) is the time in seconds that the device operates.
This formula shows that electrical energy depends on three main factors: the voltage applied, the current flowing, and the duration for which the current flows. By understanding how each of these components affects the total energy consumption, one can better grasp how electrical devices use energy.
Voltage
Voltage, also known as electric potential difference, is the "push" that makes electric charges flow through a circuit. It is measured in volts (V). Voltage can be thought of as the pressure from an electrical circuit's power source pushing charged electrons (current) through the conducting loop, enabling them to do work such as lighting a lamp or spinning a motor.Each device, like a GPS receiver, has specific voltage requirements to operate efficiently. It determines how much energy gets to each part of the circuit. A higher voltage typically means more energy is available for doing work.
In the exercise, a voltage of 9.0 V is used, which helps power the GPS receiver adequately.When analyzing electrical energy consumption, understanding voltage is crucial because it is one of the core variables in calculating energy (\(E = V \times I \times t\)). Without the right amount of voltage, a device cannot function as intended. It ensures that enough energy is transferred over time to perform the tasks required by the device.
Current
In simple terms, electric current is the flow of electric charge, typically measured in amperes (A). It is one of the key elements in an electrical circuit like the one powering the GPS receiver in the exercise. Think of current as the rate at which electric charges move through a conductor.Current is crucial because it directly affects how much electrical energy a device will consume. The current in this context is the value given by the power source and is not dependent on the device itself. It allows users to determine how robustly a device operates. For instance, a higher current may supply more energy to input devices, but it can also increase the risk of overheating if not managed properly.
In the provided exercise, the current used is 0.13 A, which helps define the total energy consumed over a set period.When combined with voltage in the electrical energy formula \(E = V \times I \times t\), current helps quantify the total energy consumed by a device over time. Understanding current allows you to better control and optimize the energy consumption in electrical devices.

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Most popular questions from this chapter

An electrical conductor designed to carry large currents has a circular cross section 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104\(\Omega\). (a) What is the resistivity of the material? (b) If the electric-field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has \(8.5 \times 10{^2}{^8}\) free electrons per cubic meter, find the average drift speed under the conditions of part (b).

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A dot h). A 50-A dot h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h, and so on. (a) What total energy can be supplied by a 12-V, 60-A dot h battery if its internal resistance is negligible? (b) What volume (in liters) of gasoline has a total heat of combustion equal to the energy obtained in part (a)? (See Section 17.6; the density of gasoline is 900 kg/m\(^3\).) (c) If a generator with an average electrical power output of 0.45 kW is connected to the battery, how much time will be required for it to charge the battery fully?

An idealized voltmeter is connected across the terminals of a 15.0-V battery, and a 75.0-\(\Omega\) appliance is also connected across its terminals. If the voltmeter reads 11.9 V, (a) how much power is being dissipated by the appliance, and (b) what is the internal resistance of the battery?

An external resistor with resistance \(R\) is connected to a battery that has emf \(\varepsilon\) and internal resistance \(r\). Let \(P\) be the electrical power output of the source. By conservation of energy, \(P\) is equal to the power consumed by \(R\). What is the value of \(P\) in the limit that \(R\) is (a) very small; (b) very large? (c) Show that the power output of the battery is a maximum when \(R = r\). What is this maximum \(P\) in terms of \(\varepsilon\) and \(r\)? (d) A battery has \(\varepsilon\) = 64.0 V and \(r =\) 4.00 \(\Omega\). What is the power output of this battery when it is connected to a resistor \(R\), for \(R =\) 2.00 \(\Omega\), \(R =\) 4.00 \(\Omega\), and \(R =\) 6.00 \(\Omega\) ? Are your results consistent with the general result that you derived in part (b)?

Nerve cells transmit electric signals through their long tubular axons. These signals propagate due to a sudden rush of Na\({^+}\) ions, each with charge \(+e\), into the axon. Measurements have revealed that typically about 5.6 \(\times\) 10\(^{11}\) Na\({^+}\) ions enter each meter of the axon during a time of 10 ms. What is the current during this inflow of charge in a meter of axon?

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