Question

In a wire of length 4m and diameter 6mm, a current of 120 amperes is passed. The potential difference across the wire is found to be $18$ volts. The resistance of the wire will be
A. \[0.15\Omega \]
B. \[0.25\Omega \]
C. \[\;6.660\Omega \]
D. None of the above

Answer 1

Hint: When current is flowing through a wire of certain voltage the current is resisted by a phenomenon called resistance. Current law states that for the potential difference $V$ is developed across a wire if $I$ current is passed through the wire.

Formula used:
\[\;V = IR\;\] (Ohm's law)
$V$=potential difference between two points.
$I$= current
$R$=resistance of material.

Complete step by step answer:
When current is flowing through a wire of some potential difference across the wire the current is resisted by a phenomenon called resistance. Ohm’s law represents the relation between voltage, current, and resistance of an electric circuit.
This law states that for the potential difference $V$ across a wire if $I$ current is passed through the wire,
\[V \propto I\]
 Or
 \[V = IR\]
Here, $R$ is the constant value for a particular material called Resistance which is used to control the overflow of current.
In the above problem given,
\[I = 120{\text{ }}amp\] and \[V = 18{\text{ }}volts\]
Applying Ohm’s law,
\[V = IR\]
\[ \Rightarrow R = \dfrac{V}{I}\]
On substituting the corresponding values,
\[ \Rightarrow R = \dfrac{{18}}{{120}}\]
On simplifying the above equation, we get
\[\Rightarrow R = 0.15\Omega \]

Therefore, the resistance of the wire is $0.15\Omega $. Hence, option (A) is the correct option.

Additional Information:
The graphical representation of ohm's law is given below:

The length and radius of a wire is needed to calculate the resistivity of the wire such that,
\[\rho = R\dfrac{l}{A}\] Where,
\[\rho \] is the resistivity, $l$ is the length, $A$ is the cross-sectional area and it is given by $\pi {r^2}$
Ohm’s law does not apply to semiconductors and insulators.

Note:
Here two extra information i.e. length and diameter are given unnecessarily. This type of information was given to distract your thought.
Resistivity is not needed here in the problem, so there is no use of length and diameter.