Answer

Verified

307.5k+ views

**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 $G$.

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

Define absolute refractive index of a medium

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Write the difference between soap and detergent class 10 chemistry CBSE

Give 10 examples of unisexual and bisexual flowers

Differentiate between calcination and roasting class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE

a Why did Mendel choose pea plants for his experiments class 10 biology CBSE