Chapter 17: Problem 8
What current does a \(50.0-\Omega\) resistance draw on \(115 \mathrm{~V} ?\)
Short Answer
Expert verified
The current is 2.3 A.
Step by step solution
01
Identify the Known Variables
From the problem statement, we know the resistance \( R \) is \( 50.0 \, \Omega \) and the voltage \( V \) is \( 115 \, \mathrm{V} \). These are the known variables needed to find the current.
02
Recall Ohm's Law
Ohm's Law is given by the equation \( V = IR \), where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance. This formula can be rearranged to solve for the current \( I \).
03
Rearrange Ohm's Law to Solve for Current
To find the current \( I \), rearrange the equation as \( I = \frac{V}{R} \). This formula will allow us to calculate the current using the given voltage and resistance.
04
Substitute Known Values into Formula
Substitute \( V = 115 \, \mathrm{V} \) and \( R = 50.0 \, \Omega \) into the formula: \[ I = \frac{115}{50.0} \].
05
Calculate the Current
Carrying out the calculation, \( I = \frac{115}{50.0} = 2.3 \, \mathrm{A} \). Thus, the current drawn by the resistance is 2.3 Amperes.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Resistance Calculation
The concept of resistance is a fundamental aspect of electrical circuits. Resistance measures how much a component, like a resistor, opposes the flow of electric current. It is measured in ohms (\(\Omega\)). In circuits, all components have some level of resistance, but resistors are specifically designed to introduce resistance into a circuit.
- Resistance can be thought of as a "roadblock" for electrons. It reduces the amount of charge that can pass through a material.
- The higher the resistance, the less current flows, given a constant voltage.
- Resistors are used to control the amount of current flowing through a circuit, which helps protect electronic components from damage due to high currents.
Voltage
Voltage, often referred to as electric potential difference, is a measure of the potential energy available to push electric charges through a circuit. Measured in volts (\(\text{V}\)), it acts as a driving force that allows current to flow.
- Voltage can be imagined as the pressure that pushes water through a pipe. Just as more pressure pushes more water, more voltage pushes more electric charge.
- It's critical to ensure that circuits are supplied with the right amount of voltage, to prevent damage to components. Too high a voltage can cause excessive current, leading to overheating or failure of components.
- In the exercise, a specific voltage of \(115\, \text{V}\) is given, which is the value of the force that pushes the electrons through the resistor.
Current Calculation
Current in a circuit is the flow of electric charge, and it is measured in amperes (\(\text{A}\)). Understanding how to calculate current is essential for applying Ohm's Law efficiently.
After computing, the result reveals that the current is \(2.3 \text{A}\). Thus, the resistor draws a current of \(2.3\) amperes when a voltage of \(115\, \text{V}\) is applied. Understanding how to calculate current is essential for ensuring that circuits function safely and effectively.
- Current can be visualized like the flow of water through a pipe, where the water molecules are analogous to moving electric charges.
- In the given problem, you are tasked with calculating the current using Ohm's Law: \(V = IR\).
After computing, the result reveals that the current is \(2.3 \text{A}\). Thus, the resistor draws a current of \(2.3\) amperes when a voltage of \(115\, \text{V}\) is applied. Understanding how to calculate current is essential for ensuring that circuits function safely and effectively.