Question

Hey guys !! Plz answer this qurstion !!

A wire of length 4m and radius 0.25mm has a resustance of 24ohm. Find the resistivity of the wire .​

Answer 1

Given :-

Length of wire = 4m

Radius = 0.25mm or 0.00025m

Resistance (R) = 24 ohm

To find:-

We have to find the resistivity of wire

Forumula used !

$\bigstar{\boxed{\sf R = \dfrac{\rho l}{A}}}$

• Where ,

R= Resistance

$\sf \rho$ = Resistivity

l = length of wire

A = Area of cross section

• First find the area of cross section

$\underline{\bigstar{\sf Area \ of \ cross \ section = \pi r^2}}$

$\longrightarrow\sf \ \ take \pi = 3.14 \\ \\ \longrightarrow\sf Area = 3.14\times (0.00025)^2 \\ \\ \longrightarrow\sf Area = 3.14\times 0.0000000625\\ \\ \longrightarrow\sf Area = 0.00000019625 \\ \\ \longrightarrow\sf\ or \ Area\ = 1.9625\times 10^{-7} m^2$

• Now find the resistivity

$\longrightarrow\sf\ R= \dfrac{\rho l}{A}\\ \\ \longrightarrow\sf 24= \dfrac{\rho \times 4}{1.9625\times 10^{-7}}\\ \\ \longrightarrow\sf 24= \dfrac{\rho \times 4\times 10^7}{1.9625}\\ \\ \longrightarrow\sf 24\times 1.9625 = \rho \times 4\times 10^7\\ \\ \longrightarrow\sf 47.1= \rho \times 4\times 10^7\\ \\ \longrightarrow\sf \dfrac{47.1}{ 4\times 10^7}= \rho \\ \\ \longrightarrow\sf\ \rho = \dfrac{\cancel{47.1}\times 10^{-7}}{\cancel{4}}\\ \\ \longrightarrow\sf\ \rho = 11.775\times 10^{-7} \Omega \ m$

$\underbrace{\bigstar{\sf{ Resistivity \ of \ wire (\rho) = 11.775\times 10^{-7} \Omega\ m}}}$

Answer 2

Answer:

Given :

• Length = 4 m.
• Radius = 0.25 mm = 0.00025 m.
• Resistance = 24 ohm.

To Find :

• Resistivity.

Solution :

Formula : R = rho*l/A

Hence, Rho = R*A/l.

Now, Finding the area of cross section :

➸ π r²

➸ 3.14 × (0.00025)²

➸ 3.14 × 0.0000000625

➸ 0.0000001963 m² = 1.963 × 10^{-7} m²

Now, Finding the resistivity :

➸ Resistivity = R*A/l

➸ Resistivity = 24* 1.963 × 10^{-7}/4

➸ Resistivity = 6 * 1.963 × 10^{-7}

➸ Resistivity = 11.778 × 10^{-7} ohm m