Ohm's Law: Understanding the Relationship Between Current and Resistance on a Graph

When you plot resistance R on the vertical axis and current I on the horizontal axis, the relationship described by Ohm's Law can be analyzed through various scenarios. Ohm's Law states that the voltage V across a resistor is directly proportional to the current through it:

V I cdot R

Rearranging this equation for resistance R gives:

R frac{V}{I}

Let's explore how the graph behaves in different scenarios based on this rearranged formula.

Constant Resistance and Ohmic Materials

For ohmic materials, the resistance is constant for a given voltage. In this case, when plotting R versus I:

Hyperbolic Curve: The graph will show a hyperbolic curve because as the current increases, the resistance remains constant. The curve will approach the vertical axis asymptotically but will never touch it. This is because the relationship between current and resistance is inversely proportional. As the current increases, the resistance calculated using R frac{V}{I} will actually decrease.

Zero Current Scenario

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Undefined Resistance: When the current I 0 , the resistance is undefined (or can be considered infinite) since you cannot divide by zero.

Increasing Current

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Decreasing Resistance: As the current I increases, the resistance R decreases and approaches zero as I increases infinitely. This characteristic behavior is typical of ohmic conductors where the material does not heat up or change its properties with increased current.

Summary of the Graph

The graph will start from a point representing high resistance (approaching infinity) as the current approaches zero and will curve downwards, approaching the horizontal axis but never touching it. This indicates that as you increase the current, the resistance decreases.

Conclusion

The graph reflects the inverse relationship between current and resistance as defined by Ohm's Law for a given voltage. The resistance does not rise or fall at a constant rate but decreases as the current increases, forming a hyperbolic curve.

Since we are obeying Ohm's Law, the value of resistance R is constant, and the value changing is that of the current. Plotting such a graph will give you a straight line parallel to the horizontal axis, meaning there will be no slope.