FIGURE EX27.35 is a current-versus-potential-difference graph for a material. What is the material's resistance?

Verified step by step guidance

1. Step 1: Recall Ohm's Law, which states that the resistance (R) of a material is given by the formula: $R=\frac{\mathrm{\Delta V}}{I}$, where ΔV is the potential difference and I is the current.
2. Step 2: Analyze the graph provided. The graph shows a linear relationship between current (I) and potential difference (ΔV), indicating that the material obeys Ohm's Law. The slope of the graph represents the reciprocal of resistance.
3. Step 3: Identify two points on the graph to calculate the slope. For example, at ΔV = 50 V, I = 1 A, and at ΔV = 100 V, I = 2 A.
4. Step 4: Calculate the slope of the graph using the formula for slope: $\frac{I}{}$₂-I₁ΔV₂-ΔV₁. Substitute the values from the graph: $\frac{2-1}{100-50}$.
5. Step 5: Once the slope is calculated, take its reciprocal to find the resistance: $R=\frac{1}{\mathrm{slope}}$. This will give the material's resistance.

Key Concepts

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points, given by the formula V = IR, where R is the resistance. This relationship is fundamental in understanding how electrical circuits operate and is crucial for calculating resistance from current and voltage values.

Resistance

Resistance is a measure of the opposition to the flow of electric current in a material. It is defined as the ratio of voltage to current (R = V/I) and is measured in ohms (Ω). In the context of the provided graph, the slope of the line represents the resistance of the material, indicating how much voltage is needed to produce a certain amount of current.

Linear Relationship

A linear relationship in a graph indicates that two variables change at a constant rate relative to each other. In the current-versus-potential-difference graph, the straight line suggests that as the voltage increases, the current increases proportionally, which is characteristic of ohmic materials. This linearity allows for straightforward calculations of resistance using the slope of the line.