Answer

Verified

408.9k+ views

**Hint:**We need to understand and apply the correct relations between the given physical parameters such as the resistance, resistivity of the material and length of the wire to find the unknown area of cross-section of the given wire to solve this problem.

**Complete answer:**

We know from Ohm's law that the resistance for a wire is the property which is constant for any range of potential drop and the corresponding current flow through the wire. From the Ohm’s law, we know that –

\[\begin{align}

& V\propto I \\

& \text{and,} \\

& V=IR \\

\end{align}\]

Here, the resistance is the constant of proportionality that balances and connects the voltage drop across the wire and the current through it.

The resistance is defined as the opposing effect experienced by the electrons in the movement under an applied external potential difference. It is dependent on the length of the wire, the area of cross-section of the wire and the nature of the wire.

From experiments, we have derived that the resistance increases with the length of the conductor and decreases with increasing area of cross-section of the wire. We can mathematically write this as –

\[\begin{align}

& R\propto \dfrac{l}{A} \\

& \Rightarrow R=\rho \dfrac{l}{A} \\

\end{align}\]

The constant of proportionality is the resistivity of the material. It is a characteristic property of the material that doesn’t change with any physical changes except for temperature.

The area of cross-section of the given resistor can be found from this relation as –

\[\begin{align}

& R=\rho \dfrac{l}{A} \\

& \Rightarrow A=\dfrac{\rho l}{R} \\

& \Rightarrow A=\dfrac{1.84\times {{10}^{-6}}\times 1}{23} \\

& \therefore A=8\times {{10}^{-8}}{{m}^{2}} \\

\end{align}\]

The area of cross-section of the given wire is –

\[A=8\times {{10}^{-8}}{{m}^{2}}\]

**Note:**

The resistance of a conducting material is dependent on the physical dimensions such as the length of the wire and it’s area of cross-section, whereas the resistivity is a material property which can change only with a change in temperature.

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE