Problem 57 - Fundamentals of Physics

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identify Given Values

In this exercise, we are given:- Power, \( P = 18.0 \text{ W} \)- Voltage, \( V = 9.00 \text{ V} \)- Time, \( t = 4.00 \text{ hours} = 4.00 \times 3600 \text{ seconds} = 14400 \text{ seconds} \)

Step 2: Calculate Current

We use the formula for power \( P = IV \), where \( I \) is the current in amperes, to find \( I \):\[ I = \frac{P}{V} = \frac{18.0 \text{ W}}{9.00 \text{ V}} = 2.00 \text{ A} \]

Step 3: Use Charge Formula

The charge \( Q \) that flows through the device can be found using the formula \( Q = It \), where \( I \) is current in amperes, and \( t \) is time in seconds:\[ Q = (2.00 \text{ A})(14400 \text{ s}) = 28800 \text{ C} \]

Step 4: Verify Units and Calculation

Ensure that each calculation used consistent units: - Current was calculated in amperes. - Time was converted to seconds (4 hours = 14400 s). - Charge is in coulombs, as expected. Thus, the calculations are correct.

Key Concepts

Electric Current

Electric current is the flow of electric charge. It is linked to the movement of electrons through a conductive material, like a metal wire. Understanding the concept of electric current is important when working with electronic devices, circuits, and electricity in general. The flow of current is measured in amperes (A) and it represents the quantity of charge passing a point in a circuit per second.
To calculate the current flowing through a device, you can use the relationship between power (P), voltage (V), and current (I). This is given by the formula \( P = IV \). Here, \( P \) is the power in watts (W), \( V \) is the voltage in volts (V), and \( I \) is the current in amperes (A). By rearranging the formula, you can find the current as \( I = \frac{P}{V} \).
In the given exercise, when we use this formula, we calculate that the electric current passing through the device is 2.00 amperes. This means every second, 2 coulombs of charge are passing through the device.

Power and Energy

Power in an electrical context is the rate at which energy is transferred or converted by a device. It is measured in watts (W), where one watt equals one joule per second. In simpler terms, power tells us how much energy a device uses over time.
Electrical devices convert electrical energy into other forms of energy like heat, light, or mechanical energy. For example, a light bulb converts electrical energy into light and heat.
The power formula \( P = IV \) is useful for evaluating the energy consumption and efficiency of devices. When you know the power, you can also determine the amount of energy used over a specific period. By multiplying power by time, you find Energy (E), which is measured in joules. The energy consumption is calculated as \( E = P \times t \), where time \( t \) is expressed in seconds.
In the exercise, the device has a power rating of 18.0 W and operates for 4 hours. The amount of energy used by the device would therefore be \( 18.0 \text{ W} \times 14400 \text{ s} = 259200 \text{ J} \). Understanding how power and energy are connected helps you manage electricity use and can guide you in choosing energy-efficient appliances.

Voltage

Voltage is the electric potential difference between two points in a circuit. It is often described as an electric pressure or force that drives the electric charge to flow within a circuit. The unit for voltage is the volt (V), and it represents the amount of energy per unit charge.
Voltage is crucial because it determines how much current will flow in a circuit for a given resistance. Ohm's Law provides the basic relationship between voltage (V), current (I), and resistance (R) in a circuit: \( V = IR \). This tells us that for a constant resistance, an increase in voltage will result in an increase in current.
In simple terms, voltage is like the push that causes an electric current to flow. High voltage means more force is driving the electrons through the circuit.
From the exercise, the device was supplied with a voltage of 9.00 V. This potential difference is a key factor in how the device operates, as it allows electricity to flow and enables the device to function efficiently. Understanding voltage can help explain how devices, like batteries or power adapters, provide the necessary energy to power electronic equipment.