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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 \(1.5 \mathrm{~h} ?\)

Short Answer

Expert verified
The GPS consumes 6318 Joules of energy in 1.5 hours.

Step by step solution

01

Find Power Consumption

First, find the power consumption of the GPS using the formula for electric power: \[ P = V imes I \] where - \( V = 9.0 \, V \) is the voltage,- \( I = 0.13 \, A \) is the current. Plug in the values: \[ P = 9.0 \, V \times 0.13 \, A = 1.17 \, W \]
02

Convert Operating Time to Seconds

Since power consumption over time is often calculated in seconds, convert the time from hours to seconds. Given time is 1.5 hours,\[ 1.5 \, ext{hours} \times 3600 \, ext{seconds/hour} = 5400 \, ext{seconds} \]
03

Calculate Energy Consumed

Use the formula for energy consumption: \[ E = P imes t \] where- \( E \) is the energy in joules,- \( P = 1.17 \, W \) is the power,- \( t = 5400 \, ext{seconds} \) is the time.Substitute the values:\[ E = 1.17 \, W \times 5400 \, s = 6318 \, J \]

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Key Concepts

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

Electric Power
Electric power is fundamental to understanding how electrical devices operate. Power, in electrical terms, is the rate at which electrical energy is consumed, transferred, or converted. It is measured in watts (W). The formula to calculate electric power is: \[ P = V \times I \]where \( P \) is the electric power in watts, \( V \) is the voltage in volts, and \( I \) is the current in amperes. This formula shows that power is directly proportional to both the voltage and the current. So, if either the voltage or the current increases, the electric power will also increase proportionally.
Electric power is what drives all our electronic devices, from small gadgets like a GPS receiver to large household appliances like refrigerators. Understanding this concept helps us to calculate and manage the energy consumption of any device efficiently.
Energy Consumption
Energy consumption refers to the total amount of energy used by an electronic device over a period of time. It is measured in joules (J) or kilowatt-hours (kWh). Calculating energy consumption is crucial for managing electricity usage and can help us understand how efficient an electronic device is. The formula used to calculate energy consumption is: \[ E = P \times t \] where \( E \) is the energy consumed in joules, \( P \) is the power in watts, and \( t \) is the time in seconds.
  • By multiplying the power by the time, we can find the total energy used during that period.
  • This calculation helps determine the cost of running electrical devices, as many energy bills are based on energy consumption in kilowatt-hours.
  • It's also useful in optimizing device usage for energy conservation.
For instance, if you know that a GPS device uses 1.17 W of power, and it runs for 1.5 hours, by using the formula you can calculate that it consumes 6318 J of energy.
Voltage and Current
Voltage and current are two fundamental elements of any electrical circuit.
Voltage, often called electric tension, is essentially the "pressure" that pushes electric charges through a conductor. It's measured in volts (V) and can be thought of as the force that moves electrons through a wire. Higher voltage means more potential energy per charge.
Current, on the other hand, is the flow of electric charge. Measured in amperes (A), current tells us how many electrons are moving past a point in the circuit per second. It’s like the flow rate of water through a pipe.
  • Together, voltage and current determine how power is delivered to electronic devices.
  • In a circuit, voltage is always applied across components, while current is what flows through them.
  • Lowering either the voltage or the current will result in reduced electric power and energy intake.
To operate any electronic device efficiently, it's important to ensure the supply voltage matches the device requirements and the current rating is not exceeded, which can prevent overheating and improve lifespans.

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Most popular questions from this chapter

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