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Chapter 7: Problem 34

The formula \(R=\frac{V}{I}\) represents the relationship of the resistance \(R\), voltage \(V\), and current \(I\) in an electric circuit. Assume that \(V\) is constant. Is the relationship of \(R\) and \(I\) a direct variation or an inverse variation?

Short Answer

Expert verified
Inverse variation.

Step by step solution

01

Identify the given formula

The given formula is \(R = \frac{V}{I}\), which represents the relationship between resistance (R), voltage (V), and current (I) in an electric circuit.
02

Determine the constant

Voltage (V) is given as constant in the problem statement.
03

Express the formula in terms of constants and variables

Rewrite the formula by acknowledging that V is a constant: \(R = \frac{V}{I}\). Here, R is the dependent variable, and I is the independent variable.
04

Analyze the relationship

In the formula \(R = \frac{V}{I}\), as the current (I) increases, the resistance (R) decreases, assuming that V is constant. Conversely, as I decreases, R increases.
05

Classify the type of variation

Since an increase in I results in a decrease in R, and a decrease in I results in an increase in R, this is an example of inverse variation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ohm's Law
Ohm's Law is fundamental in understanding electric circuits. The law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points. This relationship is mathematically expressed as \( V = IR \).

Here:
  • \( V \) represents voltage
  • \( I \) stands for current
  • \( R \) denotes resistance
Using Ohm's Law, we can understand how changing one variable affects the others in the circuit. For example, if you increase the voltage across a resistor, the current through the resistor will also increase if the resistance remains constant.
Electric Circuits
An electric circuit is a closed path through which an electric current flows. An electric circuit typically includes:
  • A power source (like a battery)
  • Conductors (wires)
  • Loads (such as resistors)

In any electric circuit, Ohm's Law, which we discussed before, helps to predict how much current will flow based on the voltage and resistance in the circuit. By manipulating the components in a circuit, you can control the electricity to perform useful work.
Inverse Relationships
An inverse relationship occurs when one variable increases while the other decreases. In the context of electric circuits, we can see an inverse relationship between resistance (\( R \)) and current (\( I \)) when voltage (\( V \)) is constant.

The formula \( R = \frac {V}{I} \) from Ohm's Law illustrates this:
  • If the current \( I \) increases, the resistance \( R \) must decrease if \( V \) remains constant.
  • Conversely, if the current \( I \) decreases, the resistance \( R \) will increase.

This inverse relationship demonstrates how different components in an electric circuit interact with one another.
Resistance and Current
In an electric circuit, resistance (denoted as \( R \)) is a measure of how much an object opposes the flow of electric current. The unit of resistance is the ohm (惟). Current (\( I \)) is the flow of electric charge, measured in amperes (A).

According to the formula \( R = \frac{V}{I} \):
  • High resistance means less current for a given voltage
  • Low resistance means more current for the same voltage

Understanding resistance and current helps in designing electric circuits efficiently. For instance, adding resistors can limit current flow to protect sensitive components in the circuit.
Voltage
Voltage (denoted as \( V \)) is the electric potential difference between two points in a circuit. It is the driving force that pushes the electric current through the circuit. Voltage is measured in volts (V).

It's important to understand that in Ohm's Law:
  • If the voltage across a circuit is held constant, changing the resistance will change the current.
  • If the resistance is held constant, changing the voltage will alter the current accordingly.

With stable voltage, other components like resistance and current can be controlled more predictably, making it a crucial factor in circuit design and analysis.

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Most popular questions from this chapter

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