Question

In: Physics

The rectangular block below has front-face dimensions of 10 cm by 4 cm, with a depth...

The rectangular block below has front-face dimensions of 10 cm by 4 cm, with a depth of 3 cm.(Figure 1) You will be asked to treat this object as an electrical resistor.

no title provided

Rank the block based on its electrical resistance along the three illustrated coordinate directions (x, y, and z).

Rank from largest to smallest. To rank items as equivalent, overlap them.

PART B:

If all of the dimensions of the block double (to become 20 cm wide, 8 cm tall, and 6 cm deep), what happens to the resistance along each axis?

	The resistance quadruples.
	The resistance doubles.
	The resistance stays the same.
	The resistance is halved.
	The resistance is quartered.

Expert Solution

Concepts and reason

The concept used to solve this problem is resistance and its dependence on resistivity, length and area of the conductor.

Rank the block based on resistance dependence on length. Calculate the resistance of the block along x axis using the expression for resistance.

Fundamentals

The resistance of a conductor is defined as the property of the conductor that opposes the flow of current through it.

The expression for resistance is given as:

Rεp-
Α

Here, R is the resistance of the block, A is the area, l is the length and is the resistivity of the material.

It is measured in Ohm.

The resistance depends on length and area of cross-sectional area of the conductor.

(A)

The length of the block along the x axis is 3 cm.

The resistance for the length 3 cm is,

R 3 cmP
A

The length of the block along the y axis is 10 cm.

The resistance for the length 10 cm is,

R 10 cm

The length of the block along the z axis is 4 cm.

The resistance for the length 4 cm is,

R. =4 cm

As the resistance is directly proportional to the length of the block, the length along the y axis is greater than z axis greater than x axis.

Therefore, ranking the resistance from largest and smallest is R, R> R .

[Part A]

(B)

The resistance of the block is given as,

Rεp-
Α

The resistance of the block is,

…… (1)

Substitute 20 cm for l and 8 cm for b in the expression A lxb .

A
20 cmx8 cm
=160 cm2

The resistance of the block is,

…… (2)

Compare the equations (1) and (2), as the area gets doubles the resistance reduces by half.

[Part B]

Ans: Part A

The order is R, R> R

Part B

The resistance is halved.

genius_generous answered 2 years ago

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