Question

The breadth and height of a metallic cuboid are equal and the length of the cuboid is twice that of its breadth. The ratio of the maximum and the minimum resistances between
parallel faces is :​

Answer 1

Answer:

B=h

Let b=x=h

L=2x

Given

L*b*h=2x*x*x

2x³

Explanation:

Sorry what is minimum and maximum resistances

Answer 2

The ratio of the maximum and the minimum resistances between  parallel faces is 4.

Explanation:

Given data

• Given metallic cuboid is a a square prism. Which length ,breadth and height are given as

        Let Breadth = X

        Height = X

        Length = 2 X

• We know about square prism that four face are rectangle while other two face are square.

        Area of rectangle face = 2 X²

        Area of square face = X²

• Resistance is depend on resistivity of material ,length and cross-sectional area. Where cross-sectional area is perpendicular to current. While in this case current is perpendicular to square face or perpendicular to rectangle face.

• First case ,when current is perpendicular to square face

        We take

        Area (A) = X²

        Length along which current flow (L) = 2 X

        Resistivity of material = $\mathbf{\rho }$

        By formula of resistance

        $\mathbf{R_{1}=\rho \frac{L}{A}=\rho \frac{2X}{X^{2}}=\frac{2\rho }{X}}$      ...1)

• Second case ,when current is be perpendicular to rectangle face

        We take

        Area (A) = 2 X²

        Length along which current flow (L) = X

        Resistivity of material = $\mathbf{\rho }$

        By formula of resistance

        $\mathbf{R_{2}=\rho \frac{L}{A}=\rho \frac{X}{2X^{2}}=\frac{\rho }{2X}}$      ...2)

• Here we see that

        $\mathbf{R_{1}=R_{max}=\frac{2\rho }{X}}$

        $\mathbf{R_{2}=R_{min}=\frac{\rho }{2X}}$

• Taking the ratio of maximum resistance to minimum resistance

         $\mathbf{\frac{R_{max}}{R_{min}}=\frac{\frac{2\rho }{X}}{\frac{\rho }{2X}}=4}$