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Ch 27: Current and Resistance
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 27: Current and ResistanceProblema 35
Capitolo 27, Problema 35

FIGURE EX27.35 is a current-versus-potential-difference graph for a material. What is the material's resistance?
Graph showing current (I) in amperes versus potential difference (ΔV) in volts, illustrating a linear relationship.

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1
Step 1: Recall Ohm's Law, which states that the resistance (R) of a material is given by the formula: R=ΔVI, where ΔV is the potential difference and I is the current.
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.
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.
Step 4: Calculate the slope of the graph using the formula for slope: I2-I1ΔV2-ΔV1. Substitute the values from the graph: 2-1100-50.
Step 5: Once the slope is calculated, take its reciprocal to find the resistance: R=1slope. This will give the material's resistance.

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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.
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Resistance and Ohm's Law

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.
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Resistivity & Resistors in Circuits

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.
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Linear Thermal Expansion
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