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A $4$ ohm resistance wire is doubled on it. Calculate the new resistance of the wire.

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Last updated date: 14th Jul 2024
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Answer
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Hint:When wire is doubled it means wire is folded. As the wire is folded around so its length becomes half and area of cross section becomes twice. Resistance is the property of conductors by virtue of which it opposes the flow of electric current through it.

Complete step by step answer:
Resistance is the ratio of voltage applied to the electric current flowing through it.
$R=\dfrac{V}{I}$
Materials which have very low resistance are called conductors while materials which have very high resistance are called insulators. This is because as resistance is high flow of current becomes minimal. SI unit of resistance is ohm$(\Omega )$. $1$ohm is defined as the resistance of a conductor with a potential difference of $1$volt applied to the ends through which $1$ Ampere current flows.

Resistance mainly depends on 3 factors: Length of conductor, Area of cross section and nature of material. Resistance is directly proportional to length of wire, inversely proportional to area of cross section. Formula of resistance is:
$R=\rho \dfrac{l}{A}$
where $\rho $is known as resistivity.

Resistivity is the measure of how much an electrical conductor opposes the flow of current through it. SI unit of resistivity is ohms metre$(\Omega -m)$. In the question it is given that wire is doubled. This means to fold the wire. As the wire is folded once its length becomes halved and the area of cross section becomes twice.
Let $R$ be the original resistance: $R=\rho \dfrac{l}{A}$
Let new resistance be: ${{R}_{n}}=\rho \dfrac{{l}/{2}\;}{2A}=\rho \dfrac{l}{4A}$
Now, substituting $\rho \dfrac{l}{A}$ as $R$
${{R}_{n}}=\dfrac{R}{4}=\dfrac{4}{4}=1\Omega $..............$(R=4\Omega )$

Hence, when a $4$ ohm resistance wire is doubled then its new resistance becomes $1$ ohm.

Note:When length of wire is doubled then new resistance becomes twice but when area of cross is doubled then new resistance becomes half the original resistance. Inverse of resistance is known as conductance and the inverse of resistivity is known as conductivity.Conductance is denoted by $G$.