Question

1. You have an aluminum bar of dimensions 2cm*5cm*10 cm. You want to put it into electric circuit such a way that this bar will demonstrate the smallest possible resistance. You should connect your bar to the opposite faces with dimensions of:

Answer 1

( 5 x 10 ) cm

Explanation:

Given:

- The dimensions of the bar are:

( 2 x 5 x 10 ) cm

Find:

Which two faces with dimensions ( _x _ ) should be connected to get smallest possible resistance.

Solution:

- The electrical resistance R of any material with density ρ and corresponding dimensions is expressed as:

R = ρ*L / A

- Where, A: cross sectional Area

L: The length in between the two faces.

- We need to minimize the electrical resistance of the bar. For that the Area must be maximized and Length should be minimized.

- A_max & L_min ---- > R_min

(5*10) & ( 2) ------> R_min

Hence, the electrical resistance is minimized by connecting the face with following dimensions ( 5 x 10 ) cm