Problem 26 - Applied Physics

Question

A current of \(23 \overline{0} \mathrm{~A}\) is delivered to a truck starter motor. What electric energy (in joules) is used in the \(12.0\) -V system in \(2.00\) s?

Step-by-Step Solution

Answer

The electric energy used is 5520 joules.

Step 1: Understand the Formula for Electric Energy

Electrical energy in joules can be calculated using the formula \( E = V \cdot I \cdot t \), where \( V \) is the voltage in volts, \( I \) is the current in amperes, and \( t \) is the time in seconds. In this problem, we have \( V = 12.0 \) volts, \( I = 230 \) amperes, and \( t = 2.00 \) seconds.

Step 2: Apply Given Values into the Formula

Substitute the given values into the formula: \( E = 12.0 \text{ V} \times 230 \text{ A} \times 2.00 \text{ s} \). This will yield the electric energy used in joules.

Step 3: Perform the Calculation

Now, calculate the expression: \( 12.0 \times 230 \times 2.00 = 5520 \). Thus, the electric energy used is \( 5520 \) joules.

Key Concepts

Electric Current

Electric current is the flow of electric charge. Imagine it like water flowing through a pipe. Just as water needs a path to move from one place to another, electric charges need a conductor, like a wire, to flow through. The flow of these charges is what we call current.
The unit to measure electric current is the Ampere, abbreviated as A. In simpler terms, the current tells us how much charge is flowing through the circuit at any moment.
Consider a wire: the more electrons (or charges) that flow through the wire in a second, the higher the current. Current in circuits:

• A high current means more electric charge is flowing.
• A low current means less electric charge flows.

In the problem we looked at, a current of 230 A flows through the truck's motor. That's quite a lot, meaning the motor has a strong flow of electric charge, necessary for starting the vehicle engine.

Voltage

Voltage can be thought of as the pressure pushing the electric charges through a circuit, similar to how a pump pushes water through pipes. The more voltage, the more electric energy is available to move charges.
Measured in volts (V), voltage is the force that moves electrons in a circuit.
It's essentially what "drives" the current to flow through the circuit. Without voltage, charges wouldn't move effectively, much like water wouldn't flow without pressure.
Understanding voltage:

• Higher voltage means higher potential for doing electrical work.
• Lower voltage means less potential for doing work.

In this exercise, the 12.0-V system shows the electromotive force (EMF) provided to the truck's motor. This is the driving force that moves the large current of 230 A through the motor, enabling it to function effectively.

Joules

Joules is the unit of measure for energy. In the context of electricity, energy measured in joules tells us how much work the electric current can do. For example, powering an engine or lighting a bulb.
It's important to understand that energy and power are closely linked, but are not the same. Energy is the capacity to do work, while power is the rate at which work is done.
Joules in electrical energy:

• The larger the number of joules, the more energy is available.
• It gives us an understanding of how much electricity is consumed or transformed.

In our provided problem, the calculation showed that 5520 joules of energy was used by the truck's motor. This measurement shows substantial energy was involved, derived from the 12.0-V voltage operating over 2 seconds.

Electrical Formulas

Electrical formulas are key to understanding how electricity behaves and performs work. In our exercise, we used the formula to calculate electric energy: \[ E = V \cdot I \cdot t \]Each component of the formula plays its own role:

• \(E\) - Electric Energy in Joules: Represents the total energy used or supplied.
• \(V\) - Voltage in Volts: Provides the force or pressure in the circuit.
• \(I\) - Current in Amperes: Measures the flow of electric charge.
• \(t\) - Time in Seconds: The duration for which power is consumed.

By inserting known values into the formula, you can determine the missing one, which simplifies the process of solving electrical issues. This versatility makes electrical formulas powerful tools for both predicting and understanding electrical behavior and consumption. In our exercise, with the values given, solving for electric energy provided clear insights into the system’s power usage.