Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 7

The values of current \(I\) flowing in a given resistor for the corresponding values of potential difference \(V\) across the resistor are given below \(\begin{array}{l}I \text { (amperes) } & 0.5 & 1.0 & 2.0 & 3.0 & 4.0 \\ V \text { (volts) } & 1.6 & 3.4 & 6.7 & 10.2 & 13.2\end{array}\) Plot a graph between \(V\) and \(I\) and calculate the resistance of that resistor.

Short Answer

Expert verified
The resistance of the resistor is approximately 3.31 Ω.

Step by step solution

01

Understand the Data

Review the given values of current (I) in amperes and the potential difference (V) in volts. Note that you have pairs of values (I, V) for this exercise.
02

Plot the Graph

Create a graph with the current (I) on the x-axis and the potential difference (V) on the y-axis. Plot the given points: (0.5, 1.6), (1.0, 3.4), (2.0, 6.7), (3.0, 10.2), (4.0, 13.2). Draw a line or curve to best fit through these points.
03

Calculate the Slope of the Line

Determine the slope (m) of the best fit line. The slope of the line in a V vs. I graph represents the resistance (R) of the resistor. Use the formula for the slope: \(m = \frac{{\Delta V}}{{\Delta I}}\).
04

Pick Two Points on the Line

Use two points from the line to calculate the slope. For example, take points (0.5, 1.6) and (4.0, 13.2).
05

Calculate Resistance (R)

Use the slope formula with your chosen points: \(R = \frac{{13.2 - 1.6}}{{4.0 - 0.5}} = \frac{{11.6}}{{3.5}}\) which simplifies to approximately \(R = 3.31 \, \Omega\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

Resistance Calculation
Resistance is a measure of how much a component, like a resistor, resists the flow of electric current. To calculate resistance, Ohm's Law is used, which states the relationship between voltage (V), current (I), and resistance (R). This relationship is defined by the formula: \(R = \frac{V}{I}\). In this exercise, you are given different pairs of current and voltage values. By plotting these on a graph and calculating the slope, you can determine the resistance of the resistor. The slope of a V-I graph directly gives us the resistance value.

For example, with the given values, the slope formula is used: \(R = \frac{13.2 - 1.6}{4.0 - 0.5}\), resulting in \(R = 3.31 \, \Omega\).
V-I Graph
A Voltage-Current (V-I) graph helps visualize the relationship between voltage and current flowing through a resistor. Here’s how to plot the graph:

  • First, draw the x-axis and y-axis. Label the x-axis as current (I) in amperes, and the y-axis as voltage (V) in volts.
  • Next, plot each given pair of values on the graph: (0.5, 1.6), (1.0, 3.4), (2.0, 6.7), (3.0, 10.2), and (4.0, 13.2).
  • Then, draw the best fit line that passes through or near these points. In our case, the points should lie approximately in a straight line, indicating a linear relationship between voltage and current, as expected from Ohm's Law.

This graph is significant because the slope of the line indicates the resistance value of the resistor. Remember that having a clear, accurate graph is crucial for determining an accurate resistance value.
Slope Determination
Determining the slope of a V-I graph is essential for calculating resistance. The slope is represented by the change in voltage divided by the change in current between two points, given by the formula \(m = \frac{\Delta V}{\Delta I}\). Here are the steps:

  • Select two points from your V-I graph. Let's use (0.5, 1.6) and (4.0, 13.2).
  • Calculate the difference in the y-values (voltage): \(\Delta V = 13.2 - 1.6 = 11.6\).
  • Calculate the difference in the x-values (current): \(\Delta I = 4.0 - 0.5 = 3.5\).
  • Determine the slope: \( m = \frac{11.6}{3.5} \approx 3.31 \).

This slope value of approximately 3.31 indicates the resistance in ohms (\( R \)). Thus, the resistance of the resistor is \( 3.31 \, \Omega \). Slope determination is a straightforward method that combines graphical analysis with mathematical calculation, providing a clear understanding of the resistor's properties.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A copper wire has diameter \(0.5 \mathrm{~mm}\) and resistivity of \(1.6 \times 10^{-8} \Omega \mathrm{m}\). What will be the length of this wire to make its resistance \(10 \Omega ?\) How much does the resistance change if the diameter is doubled?

Which of the following terms does not represent electrical power in a circuit? (a) \(I^{2} R\) (b) \(I R^{2}\) (c) \(V I\) (d) \(V^{2} / R\)

Two lamps, one rated \(100 \mathrm{~W}\) at \(220 \mathrm{~V}\), and the other \(60 \mathrm{~W}\) at \(220 \mathrm{~V}\), are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is \(220 \mathrm{~V} ?\)

When a 12 V battery is connected across an unknown resistor, there is a current of \(2.5 \mathrm{~mA}\) in the circuit. Find the value of the resistance of the resistor.

Several electric bulbs designed to be used on a \(220 \mathrm{~V}\) electric supply line, are rated \(10 \mathrm{~W}\). How many lamps can be connected in parallel with each other across the two wires of \(220 \mathrm{~V}\) line if the maximum allowable current is \(5 \mathrm{~A}\) ?
See all solutions

Recommended explanations on Physics Textbooks

Astrophysics

Read Explanation

Measurements

Read Explanation

Electricity

Read Explanation

Engineering Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Medical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free