Assingment 29

#$&*

course PHY 232

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-

by-phrase interpretation of the problem along with a statement of what you do or do not

understand about it. This response should be given, based on the work you did in completing

the assignment, before you look at the given solution.

029. `Query 29

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Question: `qQuery introductory problem set 54 #'s 8-13

Explain how to determine the magnetic flux of a uniform magnetic field through a plane loop of

wire, and explain how the direction of the field and the direction of a line perpendicular to

the plane of the region affect the result.

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Your Solution:

Basically we find the area of the plane loop of wire, if given the radius find the area using

(pi*r^2) then multiply the area of the loop by the strength of the field.

Hence, we get the strength of the flux and if perpendicular to the loop then its at a non zero

angle with the field, then we mutiply the previous reasult by cosine of the angle.

confidence rating #$&*:

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Given Solution:

To do this we need to simply find the area of the plane loop of wire. If we are given the

radius we can find the area using

Pi * r ^2

Then we multiply the area of the loop (In square meters ) by the strength of the field (in

tesla).

This will give us the strength of the flux if the plane of the loop is perpendicular to the

field. If the perpendicular to the loop is at some nonzero angle with the field, then we

multiply the previous result by the cosine of the angle.

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Self-critique (if necessary):

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Self-critique Rating:ok

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Question: `qExplain how to determine the average rate of change of magnetic flux due to a

uniform magnetic field through a plane loop of wire, as the loop is rotated in a given time

interval from an orientation perpendicular to the magnetic field to an orientation parallel to

the magnetic field.

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Your Solution:

First of all we get the area of the loop and then multiply the area of the loop m^2 by the

strength of the field to find the flux when its perpendicular. As for the parallel use the

same procedure which we end up with flux 1 and 2 which if subtracted and divided by time gives

us the average rate of change if magnetic flux

confidence rating #$&*:

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Given Solution:

** EXPLANATION BY STUDENT:

The first thing that we need to do is again use Pi * r ^ 2 to find the area of the loop. Then

we multiply the area of the loop (m^2) by the strength of the field (testla) to find the flux

when the loop is perpendicular to the field.

Then we do the same thing for when the loop is parallel to the field, and since the cos of

zero degrees is zero, the flux when the loop is parallel to the field is zero. This makes

sense because at this orientation the loop will pick up none of the magnetic field.

So now we have Flux 1 and Flux 2 being when the loop is perpendicular and parallel,

respectively. So if we subtract Flux 2 from flux 1 and divide this value by the given time in

seconds, we will have the average rate of change of magnetic flux. If we use MKS units this

value will be in Tesla m^2 / sec = volts. **

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Self-critique (if necessary):

Alittle different approach but same idea.

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Self-critique Rating:ok

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Question: `qExplain how alternating current is produced by rotating a coil of wire with

respect to a uniform magnetic field.

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Your Solution:

When you rotate a coil of wire end over end inside a uniform magnetic field. When the coil is

parallel to the magnetic field, then there is no magnetic flux, and the current will be zero.

But then when the coil is perpendicular to the field or at 90 degrees to the field then the

flux will be strongest and the current will be moving in one direction. Then when the coil is

parallel again at 180 degrees then the flux and the current will be zero. Then when the coil

is perpendicular again at 270 degrees, then the flux will be at its strongest again but it

will be in the opposite direction as when the coil was at 90 degrees. So therefore at 90

degrees the current will be moving in one direction and at 270 degrees the current will be

moving with the same magnitude but in the opposite direction.

Which can be summed up as the changing of magnetic flux produces voltage which in turn

produces current

confidence rating #$&*:

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Given Solution:

** STUDENT RESPONSE WITH INSTRUCTOR COMMENT: Y

ou rotate a coil of wire end over end inside a uniform magnetic field. When the coil is

parallel to the magnetic field, then there is no magnetic flux, and the current will be zero.

But then when the coil is perpendicular to the field or at 90 degrees to the field then the

flux will be strongest and the current will be moving in one direction. Then when the coil is

parallel again at 180 degrees then the flux and the current will be zero. Then when the coil

is perpendicular again at 270 degrees, then the flux will be at its strongest again but it

will be in the opposite direction as when the coil was at 90 degrees. So therefore at 90

degrees the current will be moving in one direction and at 270 degrees the current will be

moving with the same magnitude but in the opposite direction.

COMMENT:

Good. The changing magnetic flux produces voltage, which in turn produces current. **

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Self-critique (if necessary):

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Self-critique Rating:ok

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Question: `qQuery Principles and General College Physics 18.04. 120V toaster with 4.2 amp

current. What is the resistance?

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Your Solution:

Since we know that V=IR we can rearrange the equation and solve for R therefore R=V/I

120V/4.2A=28.6ohms

confidence rating #$&*:

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Given Solution:

current = voltage / resistance (Ohm's Law). The common sense of this is that for a given

voltage, less resistance implies greater current while for given resistance, greater voltage

implies greater current. More specifically, current is directly proportional to voltage and

inversely proportional to resistance. In symbols this relationship is expressed as I = V / R.

In this case we know the current and the voltage and wish to find the resistance. Simple

algebra gives us R = V / I. Substituting our known current and voltage we obtain

R = 120 volts / 4.2 amps = 29 ohms, approximately.

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Self-critique (if necessary):

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Self-critique Rating:ok

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Question: `qQuery Principles and General College Physics 18.28. Max instantaneous voltage to a

2.7 kOhm resistor rated at 1/4 watt.

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Your Solution:

We know that V=IR based by ohms law then P=VI=V^2/R so solving for V_max=sqrt(P*R)=sqrt

(1/4W*2.7*10^3 ohms)=26V

confidence rating #$&*:

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Given Solution:

Voltage is energy per unit of charge, measured in Joules / Coulomb.

Current is charge / unit of time, measured in amps or Coulombs / second.

Power is energy / unit of time measured in Joules / second.

The three are related in a way that is obvious from the meanings of the terms. If we multiply

Joules / Coulomb by Coulombs / second we get Joules / second, so voltage * current = power. In

symbols this is power = V * I.

Ohm's Law tells us that current = voltage / resistance.In symbols this is I = V / R. So our

power relationship power = V * I can be written

power = V * V / R = V^2 / R.

Using this relationship we find that

V = sqrt(power * R), so in this case the maximum voltage (which will produce the 1/4 watt

maximum power) will be

V = sqrt(1/4 watt * 2.7 * 10^3 ohms) = 26 volts.

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Self-critique (if necessary):

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Self-critique Rating:Ok

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Question: `qQuery general college physics problem 18.39; compare power loss if 520 kW

delivered at 50kV as opposed to 12 kV thru 3 ohm resistance.** The current will not be the

same at both voltages.

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Your Solution:

The 10.4 amp current will result in a voltage drop of 10.4 amp * 3 ohms = 31.2 volts.

The 43.3 amp current will result in a voltage drop of 40.3 amp * 3 ohms = 130 volts.

The power loss through the transmission wire is the product of the voltage ( J / C ) and the

current (J / S) so we obtain power losses as follows:

At 520 kV the power loss is 31.2 J / C * 10.4 C / s = 325 watts, approx. At 12 kV the power

loss is 130 J / C * 43.3 C / s = 6500 watts

confidence rating #$&*:

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Given Solution:

It is important to understand that power (J / s) is the product of current (C / s) and voltage

(J / C).

So the current at 50 kV kW will be less than 1/4 the current at 12 kV.

To deliver 520 kW = 520,000 J / s at 50 kV = 50,000 J / C requires current I = 520,000 J/s /

(50,000 J/C) = 10.4 amps. This demonstrates the meaning of the formula P = I V.

To deliver 520 kW = 520,000 J / s at 12 kV = 12,000 J / C requires current I = 520,000 J/s /

(12,000 J/C) = 43.3 amps.

The voltage drops through the 3 Ohm resistance will be calculated as the product of the

current and the resistance, V = I * R:

The 10.4 amp current will result in a voltage drop of 10.4 amp * 3 ohms = 31.2 volts.

The 43.3 amp current will result in a voltage drop of 40.3 amp * 3 ohms = 130 volts.

The power loss through the transmission wire is the product of the voltage ( J / C ) and the

current (J / S) so we obtain power losses as follows:

At 520 kV the power loss is 31.2 J / C * 10.4 C / s = 325 watts, approx. At 12 kV the power

loss is 130 J / C * 43.3 C / s = 6500 watts, approx.

Note that the power loss in the transmission wire is not equal to the power delivered by the

circuit, which is lost through a number of parallel connections to individual homes,

businesses, etc..

The entire analysis can be done by simple formulas but without completely understanding the

meaning of voltage, current, resistance, power and their relationships it is very easy to get

the wrong quantities in the wrong places, and especially to confuse the power delivered with

the power loss.

The analysis boils down to this:

I = P / V, where P is the power delivered. Ploss = I^2 R, where R is the resistance of the

circuit and Ploss is the power loss of the circuit.

So Ploss = I^2 * R = (P/V)^2 * R = P^2 * R / V^2.

This shows that power loss across a fixed resistance is inversely proportional to square of

the voltage. So that the final voltage, which is less than 1/4 the original voltage, implies

more than 16 times the power loss.

A quicker solution through proportionalities:

For any given resistance power loss is proportional to the square of the current.

For given power delivery current is inversely proportional to voltage.

So power loss is proportional to the inverse square of the voltage.

In this case the voltage ratio is 50 kV / (12 kV) = 4.17 approx., so the ratio of power losses

is about 1 / 4.17^2 = 1 / 16.5 = .06.

Note that this is the same approximate ratio you would get if you divided your 324.5 watts by

5624.7 watts. **

STUDENT COMMENT

This is confusing. I will have to keep reading over the problem until I understand the

solution….I’m afraid that I will have problems with this test…we will see…….

INSTRUCTOR RESPONSE

The concept of thinking these ideas through in terms of the units is developed in the

introductory problem sets, and may be helpful. A key idea here is that power (which you should

understand is energy / time interval, measured in Joules/second or watts) is the product of

current (in C / sec or amps) and voltage (in J / C or volts). If you multiply the number of

Coulombs per second, by the number of Joules per Coulomb, you get the number of Joules per

second.

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Self-critique (if necessary):

I get the relationship between Power,resistance,current and volatage but why not just obatin

the currents and compare?

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Self-critique Rating:Not sure

@&

If you fully understand why the power, for a given resistance, is proportional to the square of the current, you could just square the ratio of the currents.

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Question: `qQuery univ students with 12th and later editions should attempt this problem

before reading the solution; 11th edition 25.62 (26.50 10th edition) A rectangular block of a

homogeneous material (i.e., with constant resistivity throughout) has dimensions d x 2d x 3d.

We have a source of potential difference V.

To which faces of the solid should the voltage be applied to attain maximum current density

and what is the density?

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Your Solution:

The resistance of the block is proportional to the distance between faces and inversely

proportional to the area, so current is proportional to the area and inversely proportional to

the distance between faces. Current density is proportional to current and inversely

proportional to the area of the face, so current density is proportional to area and inversely

proportional to the distance between faces and to area, leaving current inversely proportional

to distance between faces.

For the faces measuring d x 2d we have resistance R = rho * L / A = rho * (3d) / (2 d^2) = 3 /

2 rho / d so current is I = V / R = V / (3/2 rho / d) = 2d V / (3 rho).

Current density is I / A = (2 d V / (3 rho) ) / (2 d^2) = V / (3 rho d) = 1/3 V / (rho d).

For the faces measuring d x 3d we have resistance R = rho * L / A = rho * (2d) / (3 d^2) = 2 /

3 rho / d so current is I = V / R = V / (2/3 rho / d) = 3 d V / (2 rho).

Current density is I / A = (3 d V / (2 rho) ) / (3 d^2) = V / (2 rho d) = 1/2 V / (rho d).

For the faces measuring 3d x 2d we have resistance R = rho * L / A = rho * (d) / (6 d^2) = 1 /

6 rho / d so current is I = V / R = V / (1/6 rho / d) = 6 d V / (rho).

Current density is I / A = (6 d V / (rho) ) / (6 d^2) = V / (rho d) = V / (rho d).

Max current density therefore occurs when the voltage is applied to the largest face.

confidence rating #$&*:

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Given Solution:

** First note that the current I is different for diferent faces.

The resistance of the block is proportional to the distance between faces and inversely

proportional to the area, so current is proportional to the area and inversely proportional to

the distance between faces. Current density is proportional to current and inversely

proportional to the area of the face, so current density is proportional to area and inversely

proportional to the distance between faces and to area, leaving current inversely proportional

to distance between faces.

For the faces measuring d x 2d we have resistance R = rho * L / A = rho * (3d) / (2 d^2) = 3 /

2 rho / d so current is I = V / R = V / (3/2 rho / d) = 2d V / (3 rho).

Current density is I / A = (2 d V / (3 rho) ) / (2 d^2) = V / (3 rho d) = 1/3 V / (rho d).

For the faces measuring d x 3d we have resistance R = rho * L / A = rho * (2d) / (3 d^2) = 2 /

3 rho / d so current is I = V / R = V / (2/3 rho / d) = 3 d V / (2 rho).

Current density is I / A = (3 d V / (2 rho) ) / (3 d^2) = V / (2 rho d) = 1/2 V / (rho d).

For the faces measuring 3d x 2d we have resistance R = rho * L / A = rho * (d) / (6 d^2) = 1 /

6 rho / d so current is I = V / R = V / (1/6 rho / d) = 6 d V / (rho).

Current density is I / A = (6 d V / (rho) ) / (6 d^2) = V / (rho d) = V / (rho d).

Max current density therefore occurs when the voltage is applied to the largest face. **

STUDENT QUESTION

I don’t really understand why current isn’t constant throughout the object. I can follow the

solution, but I don’t understand that one point. My solution was based on the constant current

which I see is not correct.

INSTRUCTOR RESPONSE

If the voltage is applied to different faces then you will get different currents.

The potential gradient is greater if the faces are closer together. This effect would tend to

result in greater current for faces that are closer together.

If the faces are closer together the areas of the faces will be greater, so the cross-

sectional area will be greater. This effect would result in greater current.

So the faces closest to together will experience the greatest potential gradient, and result

in the greatest cross-sectional area, resulting in the greatest current.

However the question asks about current density, not current.

Intuitively, we know that the potential gradient is the electric field responsible for

accelerating the charges, so that the charge density will just be proportional to the

potential gradient, so that if the voltage is applied to the faces with the least separation

the current density will be the greatest. In fact, since the separations are d, 2d and 3d we

can see that the potential gradients will be V / d, 1/2 V / d and 1/3 V / d so the other two

current densities will be 1/2 and 1/3 as great as the maximum.

This can be worked out symbolically for the general case:

R = rho * L / A,

and current is

I = V / R = V * A / (rho L)

so current density is

I / A = V / (rho L)

The greatest current density occurs for the least value of L, which for the given situation is

d, the separation between the largest faces.

Working out the details more fully is be unnecessary but might be instructive:

The faces closest together are separated by distance d, and have cross-sectional area 2 d * 3

d = 6 d^2. So the resistance is

R = rho * L / A = rho * d / (6 d^2) = rho / (6 d) = 1/6 * rho / d

The faces furthest apart are separated by distance 3d, and have cross-sectional area d * 2 d =

2 d^2. So the resistance is

R = rho * L / A = rho * d / (2 d^2) = rho / (2 d) = 1/2 * rho / d

Similar analysis shows that the resistance between faces separated by 2 d is rho / (3/2 d) =

2/3 * rho / d.

Thus the currents would be

I = V / R = 6 V * d / rho for the closest faces

I = V / R = 2 V d / rho for the most widely separate faces

and

I = V / R = 2 /3 V d / rho for the in-between separation.

The respective current densities, current / area, would be

(6 V d / rho) / (6 d^2) = V / (rho d)

(2 V d / rho) / (3 d^2) = 2/3 V / (rho d)

(2/3 V d / rho) / (2d^2) = 1/3 V / (rho d).

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Self-critique (if necessary):

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Self-critique Rating:ok"

Self-critique (if necessary):

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#*&!

&#Good responses. See my notes and let me know if you have questions. &#