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.

Solutions

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

Next > < Previous

Related Solutions

A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm....

A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm. If the block is connected to a 5.4 V source across two of its opposite faces, find the following. (a) What is the maximum current the block can carry? (b) What is the minimum current the block can carry?

A closely wound rectangular coil of 80 turns has dimensions 25.0 cm by 40.0 cm.

A closely wound rectangular coil of 80 turns has dimensions 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position in which it makes an angle of 37.0 degrees with a magnetic field of 1.10 T to a position perpendicular to the field. The rotation takes 0.0600 s. What is the average emf ε induced in the coil? What is the magnitude of the average emf E induced as the coil is rotated?E= ________ V

A rectangular swimming pool has dimensions of 25 m x 9 m and a depth of...

A rectangular swimming pool has dimensions of 25 m x 9 m and a depth of 1.8 m and is full to the brim with water. Determine a) the absolute pressure at the bottom of the pool, b) the total force on the bottom of the pool, and c) the absolute pressure at point P, a point on the side of the pool just near the bottom. (Worth 2 pts)

A filtration component consists of a rectangular channel having dimensions H = 10 cm, W =...

A filtration component consists of a rectangular channel having dimensions H = 10 cm, W = 50 cm, and L = 100 cm, containing carbon pellets of diameter 5 mm, is modelled using the Ergun equation. Develop the pressure drop versus mass flowrate (for ?̇ in the range of 1 – 50 kg/s) characteristic for the following porosities (due to packing arrangement): ? = 0.5, 0.7, and 0.9. The fluid properties may be taken to be ρ = 1000 kg/m3...

A closely wound rectangular coil of 80 turns has dimensions 25.0 cm by 40.0 cm. The plane...

A closely wound rectangular coil of 80 turns has dimensions 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position in which it makes an angle of 37.0 degrees with a magnetic field of 1.10 Τ to a position perpendicular to the field. The rotation takes 0.0600 s. What is the average emf ε induced in the coil? What is the magnitude of the average emf E induced as the coil is rotated? E= ________ V

Let's consider a rectangular wave guide with dimensions of ? = 1.58 cm and ? =...

Let's consider a rectangular wave guide with dimensions of ? = 1.58 cm and ? = 0.79 cm, filled with air inside and copper outside. a) Calculate the cutoff frequency for the first three advancing modes. Specify the name of the dominant (basic) mode. b) Draw roughly the electric field and magnetic field lines in the waveguide sections (sections taken from the xy, yz and xz planes) for the basic mode. For drawing, consider that the waveguide extends in the...

You place a mirror 10 cm in front of your face, which creates an upright image...

You place a mirror 10 cm in front of your face, which creates an upright image that is twice the height of the object. You then move the mirror along the principle axis until it creates an inverted image twice the height of the object. What kind of mirror must this be and why? Where is the object with respect to the mirror’s focal length for each of the mirror positions? (ie. f < s < R) Draw ray diagrams...

a. Laser light comes in to a rectangular block of thick (12 cm) glass with an...

a. Laser light comes in to a rectangular block of thick (12 cm) glass with an incident angle (relative to normal) of 25 degrees. What angle does the light have inside and as it leaves the block, and by what distance (in cm) does it seem displaced compared to where the laser beam would be with not glass ? b If instead of laser light you were viewing an object or bug on the other side of the block, how...

A 10 cm x 10 cm x 10 cm block of steel (density of steel =7900...

A 10 cm x 10 cm x 10 cm block of steel (density of steel =7900 kg/m3) is suspended from a spring scale. The scaleis in newtons. a. What is the scale reading if theblock is in air? b. What is the scale reading after theblock has been lowered into a beaker of oil and is completelysubmerged?

In a rectangular cross-section canal with a width of 10 m and a depth of 1.5...

In a rectangular cross-section canal with a width of 10 m and a depth of 1.5 m, uniform and Continuous current monitoring is applied. The channel's Manning coefficient includes 0.015. Base because its slope is 0.0005. Considering this information a) By writing the numerical magnitude of water face slope and energy line slope and its rationale Set. b) Calculate the speed of the current in the channel. c) Calculate the flow of the current in the channel. d ) When...

Subjects