Question

The figure is a current-versus-potential-difference graph for a cylinder.

What is the cylinder's resistance?

Answer 1

Concepts and reason

The problem deals with the concept of the ohm’s law as the relation between the current and voltage is linear and the value of the resistance is to be determined.

Fundamentals

According to the ohm’s law the voltage through an ideal conductor is directly proportional to the current flowing through the conductor and the constant of the proportionality is resistance $R$ as:

$V = IR$

Here $V$ is the voltage, $I$ is the current, and $R$ is the resistance.

Since the relation between voltage and current of the cylinder is linear.

Since the relation between the change in voltage and change in current is constant which is in conditions of the ohm‘s law.

Therefore the resistance of the cylinder will be the ratio of the change in voltage in the conductor to the change in current:

$R = \frac{{\Delta V}}{{\Delta I}}$

From the ohm’s law the resistance of the cylinder will be:

$R = \frac{{\Delta V}}{{\Delta I}}$

the change is voltage is:

$\begin{array}{c}\\\Delta V = 100{\rm{ V}} - 0{\rm{ V}}\\\\ = 100{\rm{ V}}\\\end{array}$

And the change in current is:

$\begin{array}{c}\\\Delta I = 2{\rm{ A}} - 0{\rm{ A}}\\\\ = 2{\rm{ A}}\\\end{array}$

Therefore substitute the value of change in voltage $\Delta V = 100{\rm{ V}}$ and the change in current $\Delta I = 2{\rm{ A}}$ the resistance of the cylinder will be as:

$\begin{array}{c}\\R = \frac{{\Delta V}}{{\Delta I}}\\\\ = \frac{{100{\rm{V}}}}{{2{\rm{ A}}}}\\\\ = 50{\rm{ \Omega }}\\\end{array}$

Ans:

The resistance of the cylinder will be $50{\rm{ \Omega }}$ .