# The dimension of a metal block is given in the diagram

The ratio of $100cm \times 2cm \times 2cm$ resistance between square faces and rectangular faces is

(A) $1:1$

(B) \[25:1\]

(C) $2500:1$

(D) $50:1$

Answer

Verified

177.6k+ views

**Hint :**Use the formula of resistance of the conductor to find the resistance of the square face and the rectangle face. The dimensions of the block is given from that we can know the side of the square and the length and breadth of the rectangle with that find the area of the square and rectangle and substitute those values in the resistance formula then find the ratio of resistance between square faces and rectangular faces.

**Complete step by step answer**

Resistance offered to a conductor is known as resistivity. The resistivity is defined as the capability of restriction of flow of current.

The resistance of a conductor is directly proportional to the length of the conductor and is inversely proportional to its area of cross section A.

$ \Rightarrow R \propto \dfrac{l}{A}$

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

$\rho $ is the specific resistance or electrical resistivity of the conductor.

l is the length of the conductor

A is the area of the conductor

We have to find the ratio of resistance between square faces and rectangular faces.

Firstly let us calculate the resistance of the square face

The length of the side of the square, $a = 2cm$

The area of the square is $4a$

$ \Rightarrow {\text{A }} = {\text{ 4a}}$

$ \Rightarrow {\text{A }} = {\text{ }}4 \times 2$

$ \Rightarrow {\text{A }} = {\text{ 8cm}}$

We know that the resistance of a conductor is

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

$ \Rightarrow {R_s} = \dfrac{{\rho 2}}{8}$

$ \Rightarrow {R_s} = \dfrac{\rho }{4}{\text{ }} \to {\text{1}}$

Now let us calculate the resistance of the rectangular face

The length of the rectangle, $b = 100cm$

The breadth of the rectangle, $l = 2cm$

The area of the rectangle is $l \times b$

$ \Rightarrow {\text{A }} = {\text{ l}} \times {\text{b}}$

$ \Rightarrow {\text{A }} = {\text{ 2}} \times {\text{100}}$

$ \Rightarrow {\text{A }} = {\text{ 200}}$

We know that the resistance of a conductor is

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

$ \Rightarrow {R_R} = \dfrac{{\rho 2}}{{200}}$

$ \Rightarrow {R_R} = \dfrac{\rho }{{100}}{\text{ }} \to {\text{2}}$

To find the ratio of resistance between square faces and rectangular faces divide the resistance of square faces by rectangular faces

$ \Rightarrow \dfrac{{{R_s}}}{{{R_R}}} = \dfrac{{\dfrac{\rho }{4}}}{{\dfrac{\rho }{{100}}}}$

$ \Rightarrow \dfrac{{{R_s}}}{{{R_R}}} = \dfrac{\rho }{4} \times \dfrac{{100}}{\rho }$

$ \Rightarrow \dfrac{{{R_s}}}{{{R_R}}} = \dfrac{{25}}{1}$

$ \Rightarrow {R_s}:{R_R} = 25:1$

The ratio of resistance between square faces and rectangular faces is $25:1$

**Hence the correct answer is option (B) $25:1$.**

**Note**

It is a direct question if we know the basic math formulas and the resistance formula we can easily solve this problem. Most of the students mistook the breadth of the rectangle as the length of the rectangle and put wrong values in the resistance formula, so be careful while substituting the values.

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

If the distance bfs covered by a particle in time t class 11 physics JEE_Main

A spring of spring constant 5rm times rm 103Nm 1is class 11 physics JEE_Main

What are the effects of earth motion class 11 physics JEE_Main

A monoatomic gas of mass 40mu is kept in an insulated class 11 physics JEE_Main

The decrease in the potential energy of a ball of mass class 11 physics JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE