Chapter 21: Problem 4
What voltage is required to produce a current of \(0.62 \mathrm{~A}\) in a \(250-\Omega\) resistor? (Hint: Solve Ohm's law for voltage, V.)
Short Answer
Expert verified
The voltage required is 155 V.
Step by step solution
01
Understanding Ohm's Law
Ohm's Law is a fundamental principle used to find the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. It is given by the formula \[ V = I \times R \]where V is the voltage across the resistor in volts (V), I is the current through the resistor in amperes (A), and R is the resistance in ohms (Ω).
02
Identifying Given Values
From the problem statement, we are given the current I = 0.62 A and the resistance R = 250 Ω. Our goal is to find the voltage V that produces this current.
03
Applying Ohm's Law
Using Ohm's Law, substitute the given values for current (I) and resistance (R) into the formula:\[ V = 0.62 \times 250 \]
04
Calculating the Voltage
Perform the multiplication to find the voltage:\[ V = 155 \, ext{V} \]
05
Conclusion and Verification
We have calculated the voltage required to produce the desired current in the resistor as V = 155 volts. This result makes sense because increasing current and resistance should increase the voltage according to Ohm's Law.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Voltage
Voltage is a key concept in electrical circuits, representing the potential difference between two points in a circuit. It is the force that pushes electrical charges through a conductor, such as a wire. Imagine voltage as the pressure of water in a hose; the higher the pressure, the more water flows through.
In an electrical context, voltage is what drives the electric current through a circuit. It is measured in volts (V).
When working with Ohm's Law, voltage can be calculated using the formula:
In an electrical context, voltage is what drives the electric current through a circuit. It is measured in volts (V).
When working with Ohm's Law, voltage can be calculated using the formula:
- \[ V = I \times R \]
- \( V \) is the voltage in volts.
- \( I \) is the current in amperes.
- \( R \) is the resistance in ohms.
Exploring Current
Current is the flow of electric charge in a circuit. It is measured in amperes (A), often referred to simply as "amps."
Current is like the flow of water through a pipe; it is the actual movement of electrons through a conductor. This flow is crucial for making all the components in a circuit work.
In Ohm's Law, current is represented by the letter \( I \), and it plays a vital role in determining the voltage of a circuit. The relationship between current and other elements in a circuit can be visualized as:
Current is like the flow of water through a pipe; it is the actual movement of electrons through a conductor. This flow is crucial for making all the components in a circuit work.
In Ohm's Law, current is represented by the letter \( I \), and it plays a vital role in determining the voltage of a circuit. The relationship between current and other elements in a circuit can be visualized as:
- Given a constant resistance, if the current increases, more electrons are flowing, which indicates higher voltage.
- If the current is stable, changes in resistance or voltage will affect the system.
Decoding Resistance
Resistance is the opposition to the flow of electric current in a circuit. It acts like a dam holding back water, slowing down the flow of electrons during their journey through a conductor.
Resistance is expressed in ohms (Ω), named after the German physicist Georg Simon Ohm, to reflect this property.
Key points for understanding resistance include:
Resistance is expressed in ohms (Ω), named after the German physicist Georg Simon Ohm, to reflect this property.
Key points for understanding resistance include:
- The higher the resistance, the less current will pass through a conductor for a given voltage.
- Conversely, if resistance decreases, more current can flow at the same voltage.