Question

Let the resistance of an electrical component remain constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?

Answer 1

Hint:Use the expression for Ohm’s law to a current carrying electric current. This formula gives the relation between the potential difference across the ends of the current carrying conductor, electric current flowing through the conductor and is the resistance offered by the conductor to the electric current through it.

Formula used:
The expression for Ohm’s law is given by
\[V = IR\] …… (1)
Here, \[V\] is the potential difference across the two ends of the current carrying conductor, \[I\] is the electric current flowing through the conductor and \[R\] is the resistance offered by the current carrying conductor to the electric current flowing through it.

Complete step by step answer:
Let us consider \[I\] is the conduct flowing through the electric component, \[V\] is the potential difference across the two ends of the electrical component and \[R\] is the resistance offered by the electrical component to the electric current through it.

Rearrange equation (1) for electric current \[I\].
\[I = \dfrac{V}{R}\]
We have given that the resistance \[R\] of the electric component remains the same but the potential across the two ends of the electrical component is decreased to half of its initial value.

Hence, the new potential difference \[V'\] across the ends of the electrical component becomes
\[V' = \dfrac{V}{2}\]

We have asked to determine the new value of electric current flowing through the electrical component. We can determine this new value of electric current using equation (1).
Rewrite equation (1) for new potential differences across the ends of the electrical component.
\[V' = I'R\]
Rearrange the above equation for the new value of electric current \[I'\].
\[I' = \dfrac{{V'}}{R}\]
Substitute \[\dfrac{V}{2}\] for \[V'\] in the above equation
\[I' = \dfrac{V}{{2R}}\]
Substitute \[I\] for \[\dfrac{V}{R}\] in the above equation.
\[ \therefore I' = \dfrac{I}{2}\]

From the above equation, we can conclude that the new value of electric current changes to half of its former value.

Note:The students should use the proper expression for Ohm’s law to determine the changed value of electric current through the electrical component. Because this value is taken incorrectly, the final value for the electric current through the electrical component will be incorrect.