For the resistor, the plot of V vs I (with voltage on the y axis and current on the x axis) looks like:

To analyze the relationship between voltage (V) and current (I) for a resistor, we'll refer to Ohm's Law, which states that:

$V = I \cdot R$

where $V$ is the voltage across the resistor, $I$ is the current flowing through the resistor, and $R$ is the resistance in ohms (Ω).

1. ### Break Down the Problem

• Identify the type of relationship between voltage and current.
• Examine the slope of the linear plot represented by $V$ versus $I$.

2. ### Relevant Concepts

• For a resistor, the relationship between voltage and current is linear.
• The slope of the line in a V-I plot represents the resistance $R$.
• Since $V$ is on the y-axis and $I$ is on the x-axis, the slope can be expressed as:

$\text{slope} = \frac{V}{I} = R$

3. ### Analysis and Detail

• If the plot is a straight line passing through the origin (0,0), this indicates that the resistor follows Ohm's Law perfectly.
• The slope will remain constant at all points along the line, demonstrating a consistent resistance value $R$.

4. ### Verify and Summarize

To verify, if we take two points on the line, say $(I_1, V_1)$ and $(I_2, V_2)$:

$R = \frac{V_2 - V_1}{I_2 - I_1}$

The calculated resistance $R$ should remain constant regardless of the chosen points, confirming the linear relationship.

Final Answer

The plot of $V$ versus $I$ for a resistor is a straight line that passes through the origin, and the slope of this line represents the resistance $R$ in ohms, which is constant for an ideal resistor.