(a) Draw a V - I graph for a conductor obeying Ohm’s law.

(b) What does the slope of the V - I graph for a conductor represent?

(c) Draw a I - V graph for a linear resistor. What does its slope represent?

To address your questions, let's break them down step by step, focusing on the concepts of voltage (V), current (I), and their relationship as described by Ohm's law. This will help us visualize the graphs and understand their significance.

Visualizing the V - I Graph for a Conductor

First, let's consider the V - I graph for a conductor that follows Ohm's law, which states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points. This relationship can be expressed mathematically as:

V = I × R

Where R is the resistance of the conductor. In a V - I graph, we plot voltage (V) on the vertical axis and current (I) on the horizontal axis. For a linear conductor, the graph will be a straight line that passes through the origin (0,0).

Graph Representation

Here's how you would typically sketch this graph:

• Draw a set of axes with voltage (V) on the y-axis and current (I) on the x-axis.
• Since the relationship is linear, the line will start at the origin (0,0) and extend upwards to the right.
• The slope of this line represents the resistance (R) of the conductor.

Understanding the Slope of the V - I Graph

The slope of the V - I graph is crucial because it represents the resistance (R) of the conductor. Mathematically, the slope can be calculated as:

Slope = ΔV / ΔI = R

This means that for every unit increase in current, the voltage increases by a factor equal to the resistance. A steeper slope indicates a higher resistance, while a gentler slope indicates lower resistance. This relationship is fundamental in understanding how different materials conduct electricity.

Exploring the I - V Graph for a Linear Resistor

Now, let's shift our focus to the I - V graph for a linear resistor. In this case, we plot current (I) on the vertical axis and voltage (V) on the horizontal axis. For a linear resistor, the graph will also be a straight line, but it will have a different orientation compared to the V - I graph.

Graph Representation

To sketch the I - V graph:

• Draw the axes with current (I) on the y-axis and voltage (V) on the x-axis.
• Again, the line will start at the origin (0,0) and extend upwards to the right.
• The slope of this line in this orientation represents the conductance (G) of the resistor, which is the reciprocal of resistance.

Significance of the Slope in the I - V Graph

The slope of the I - V graph can be expressed as:

Slope = ΔI / ΔV = G = 1/R

Here, G is the conductance. A steeper slope indicates a higher conductance, meaning the resistor allows more current to flow for a given voltage. Conversely, a gentler slope indicates lower conductance. This relationship is essential for understanding how resistors behave in electrical circuits.

In summary, both the V - I and I - V graphs provide valuable insights into the behavior of conductors and resistors. The slope in each graph reveals important properties—resistance in the V - I graph and conductance in the I - V graph—allowing us to analyze and design electrical circuits effectively.