Chapter 22, Problem 108A

To determine

To explain: the reason why the resistance is equal to the voltage divided by current.

Explanation of Solution

Introduction:

The resistance offered by an electrical component is the ability to oppose the flow of electrons through the components. Higher the resistance of electrical components, slower is the number of electrons to flow through the component and lesser would be the current flow.

The amount of current flowing in the circuit not only depends on the type of materials it also depends on the applied voltage. The current flowing through the electrical component is directly proportional to the potential difference.

The parameter that remains constant is the resistance of the electrical component and the constant for the dependency of current and voltage is the resistance.

The current through the resistance is directly proportional to the applied potential difference. That is,

  $V\propto I$  ......(1)

Upon removing the proportionality and applying a constant, then the equation becomes the relation between current, voltage, and resistance. That is,

  $V=IR$  ......(2)

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

Rearrange the expression (2) for the resistance,

  $R=\frac{V}{I}$  ......(3)

The above equation of resistance depends on the applied potential difference and current through the electrical component.

The unit of resistance is expressed in $\Omega$ .