Question

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

Short answer

The material's resistance is$50\Omega .$

Step-by-step solution

Concept Introduction 

Material resistance is defined by the thermal resistance of insulating materials is usually described by their $R-$value, which indicates their resistance to heat flow. $R-$values less than one indicate greater insulating effectiveness. The $R-$value of insulation depends on its type, thickness, and density.

Explanation 

The current is a linear function of potential difference in the form of

$I=a\Delta V$

Where $a$is the slope of the graph.

From Ohm's law we know that

$I=\frac{U}{R},$

So, the slope is equal to

$a=\frac{1}{R}$

From this graph, the current grows by$1A$

When the potential difference grows by $50\mathrm{V}$so

$a=\frac{1\mathrm{A}}{50\mathrm{V}}$

So, we will get

$R=\frac{1}{a}$

Substitute the expression,

role="math" localid="1649067269150" $R=\left(\frac{1}{{\displaystyle \frac{1A}{50V}}}\right)$

$R=50\Omega$

Final Answer 

Hence, the material resistance is$50\Omega .$