Problem 44 - Fundamentals of Physics

Question

A student kept his \(9.0 \mathrm{~V}, 7.0 \mathrm{~W}\) radio turned on at full volume from 9:00 P.M. until 2: 00 A.M. How much charge went through it?

Step-by-Step Solution

Answer

The charge that went through the radio is 14040 Coulombs.

Step 1: Understand the Given Information

We have a radio with a voltage of \(9.0 \, \mathrm{V}\) and a power output of \(7.0 \, \mathrm{W}\). The radio was used from 9:00 P.M. to 2:00 A.M., which is an operation time of 5 hours.

Step 2: Convert Time to Seconds

First, convert the operation time from hours to seconds for easier calculations. There are 3600 seconds in an hour, so the total operation time is \(5 \times 3600 = 18000\) seconds.

Step 3: Use the Power Formula to Find Current

The formula relating power, voltage, and current is \(P = V \times I\), where \(P\) is power, \(V\) is voltage, and \(I\) is current. Rearrange to solve for current: \(I = \frac{P}{V}\). Substitute the given values: \(I = \frac{7.0 \, \mathrm{W}}{9.0 \, \mathrm{V}}\).

Step 4: Calculate the Current

Calculate the current using the values: \(I = 0.7777 \, \mathrm{A}\) (we will approximate it here as \(0.78 \, \mathrm{A}\)).

Step 5: Calculate the Charge

Charge \(Q\) can be calculated using \(Q = I \times t\), where \(t\) is the time in seconds, and \(I\) is the current we've found. So, \(Q = 0.78 \, \mathrm{A} \times 18000 \, \mathrm{s}\).

Step 6: Solve for Charge

Perform the multiplication to find the charge: \(Q = 14040 \, \mathrm{C}\).

Key Concepts

Current Calculation

When using electrical appliances, it's crucial to understand how to calculate the current flowing through a circuit. The current (\( I \)) is the flow of electric charge, usually measured in amperes (A). One way to determine the current is by using the formula that relates power (\( P \)), voltage (\( V \)), and current:

• \( P = V \times I \)

To solve for current, rearrange the equation:

• \( I = \frac{P}{V} \)

By inserting the values from the original problem, where the power is given as 7 watts (\( W \)) and the voltage is 9 volts (\( V \)), we can calculate the current.

Plugging in these numbers: \( I = \frac{7.0 \, \mathrm{W}}{9.0 \, \mathrm{V}} = 0.7777 \, \mathrm{A} \).
For simplicity, we approximate this to \( 0.78 \, \mathrm{A} \).
Understanding how to calculate current helps in various practical situations, such as determining how much power a device consumes or ensuring that a circuit is safe to operate.

Electrical Power

Electrical power is a fundamental concept in understanding how electric devices work. It represents the rate at which electrical energy is consumed in a circuit, measured in watts (\( W \)).
Power can be thought of as the product of voltage and current flowing through a device or system.

• \( P = V \times I \)

In practical terms, power gives us insight into how energy-hungry a device is. For instance, a television or radio with higher wattage consumes more energy and may cost more to operate over time than a device with lower wattage.

In the example, the radio has a power output of 7 watts, meaning it uses 7 joules of energy per second.
This understanding helps individuals make informed decisions about selecting appliances based on energy efficiency and operational costs.

Voltage

Voltage is a key concept when dealing with electrical circuits and systems. It is often likened to the pressure that pushes electric charges through a conductor. Think of voltage as the potential difference between two points in a circuit.

Measured in volts (\( V \)), voltage determines how forcefully electricity flows through a circuit. A higher voltage indicates a stronger "push," allowing more current to flow.
In our exercise, the radio's voltage is given as 9 volts.
This means there is enough electrical pressure to facilitate the flow of current through the device.

Understanding voltage is vital when designing or maintaining circuits, as it affects both the potential energy available and the safe operation of electronic devices.