DavidQD

The principle consideration here is definition of the word “feel” used in the test question. This is a subjective quality and is open to a broad range of interpretations.

When it comes to physics and other physical sciences, there is often, if not always, a need to quantify uniformly (as much as possible) a subjective quality. For example, why does a person feel hot at times then cold at other times when subjected to the same temperature?

To give a basis for understanding and eventually controlling environments, a series of equations were developed to quantify environmental effects on living beings (including animals). These equations are generally referred to as psychometric equations. The most recognized of these are the wind-chill factor and Heat index (aka humiture or humidex). Though common in usage, most do not really understand the information these equations present.

Other psychometric equations include the perception of sound and light. Though, not necessarily a psychometric equation, the decibel is used for sound energy because of the way the human ear perceives sound.

Most psychometric equations represent a rate. In the case of the wind-chill factor, it correlates the equivalent rate at which heat is removed by wind to a temperature without wind. A similar relation exists for the heat index. Though theses give values, the equation relates how a person perceives an effect relative to another effect.

The case in point for this question has more to do with how fast heat is removed from a human hand than how fast a substance change temperature for a given amount of heat. Though these two are related, they are not really the same thing.

~~D~~

... what is the "electrical resistance nature" ... if there is additional resistance than we calc the current will be lower !

There is not additional resistance. In this case, there is actually less resistance, so the current is higher.

The "electrical resistance nature" is simply the phenomena that results from the physical properties of any material to a change of temperature. In this case, it is resistance. The values are consistent with tungsten. My comments were to explain why the calculated value is different from the closest selectable value on the test.

All materials have a certain specific resistance and they change resistance according to temperature by certain amounts. Most (metal) materials have a positive resistance coefficient (negative conductance coefficient) to temperature. This is generally known as the "alpha" or “sigma” constant. The positive coefficient means the material increases in resistance to current flow as the temperature increases. For a negative coefficient the material decreases in resistance to current flow, as the temperature increases.

(The inverse of resistivity is called conductivity. There are perspectives where the use of conductivity is more suitable).

This coefficient is a hypothetical constant --though it really is not linear, meaning the rate of resistance to a given temperature will increase faster than the rate of temperature change. (Some materials become extremely nonlinear such as super conducting materials). However, for small (and often large) changes in temperature, the rate of change is usually insignificant, and a standardized value is used for basic calculations.

For tungsten the alpha" (α) constant is 0.004403 ohms per degree C. The initial reference point is 5.6E-8 ohms per meter @ 20 C. This means an increase of 227C will increase the resistance by 1 ohm uniformly across the standardized area and length.

Tungsten filaments are designed to operate near the lower end of its vaporization point to efficiently produce the greatest light per unit of energy. This is approximately 2500 to 2800 Kelvins. When a bulb is operated at a lower voltage the energy is reduced and the operation temperature drops accordingly. The temperature drop will in turn lower the resistance. The lower resistance will increase the current flow in proportion. Keep in mind, too, that as the resistance drops and the current flow increases the power also increases. At some point this reaches an equilibrium.

In the example, assume the calculated and actual current flow is different by about 0.7 amp, this would correspond to a temperature reduction of 159C per standard unit. Most (higher wattage) bulbs have a coiled filament of about 20 to 22 cm (the cross sectional area is also smaller). Without knowing accurate specifications, the calculations are somewhat arbitrary, but two to three times this temperature is reasonable.

The concepts presented here are usually covered in more detail in the advanced physics classes. The phenomena is described in part at the quantum level, how electron motion is affected and mediated by short-range spin waves known as paramagnons.

A basic analogy to describe the effect: Consider how a person might navigate across a room full of people. If the people are standing relatively still then navigating is more efficient than if the people are randomly moving around. The heat in this case corresponds to the motion of the people moving around.

~~D~~

My calculator gives only an error. What am I doing wrong? 

This is an enormous number. It is 264 digits long.

Doing this on your calculator is like using a lawnmower to pull a train . . .2 kilometers long . . .fully loaded . . . with lead.

This is a quotient and product of factorials. The numbers are too far apart to reliably use the permutation or commutation functions. Time out or Unendlich (Infinity) often pops up.

(There might be another method to solve it).

Actually, it does work (if the servers are not too busy).

Paste this into the 2.0calc:

nPr(103,(103-22))*81!

 This is a perceptive and intuitive piece of work figuring that out, Alan.

~~D~~

 you mean 194 watt not 192 ... right ? 

You are correct. (The value depicted is a typographical error) A correction is noted.

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what about the refractive  !! why the red is the least 

One (sometimes confusing) point to keep in mind, is the difference between diffraction and refraction.

Longer wavelengths –near the red zone -- are diffracted more, but they refract less. The opposite is true for shorter wavelengths.

~~D~~

Now the bulb operated at 200 v and it power is 280

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No, it did not.

The bulb operates at 280W when a potential of 240V is its source.

When the voltage is lowered to 200v the energy used is lowered in proportion. In this case the bulb is using 192 watt-hours, not 280wh.

(Note error: The 192 watt-hours should be 194 watt-hours)

Resistance is hypothetically constant. It is determined using the rated standard operating conditions. The power is known and the voltage is known. Squaring the voltage then dividing by the power yields resistance. Dividing the (now) known resistance into the 200v source yields the current (in amps). If you then take the product of the amperage (0.97) and applied source voltage(200v) this yields the power (194 watts).

Remember the bulb only uses 280 watts when the voltage is 240V.

~~D~~

Thanks Alan. The “mean-to-peak” for amplitude is helpful. (I was uncertain what applied to transverse waves).

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Interesting point on # 16.

I considered the specific heat aspect, but thought the psychometric formulas to have more weight here. Consider two substances that have a similar specific heat, but different conduction coefficients. Basically applying the same amount of heat will elevate each temperature the same amount. The rate at which these will absorb heat are different.

Though the total energy transferred for a given temperature rise is the same, the psychometric formulas would indicate a much colder “feel” by touch because the energy transfer is faster.

(I have never seen a collegiate physics test that didn’t have at least one question with ambiguity -- “The ubiquitous trick question.”)

~~D~~

The bulb when operated at rated voltage of 240V uses 280W per hour. This indicates a resistance of

 E²/P (240²)/280W = 206 ohms.

Assuming a uniform resistance, the current (I) at 200V (E), with a resistance of 206 ohms equals * E/R =I -- - -> 200/206 = =0.972* The correct answer is 0.98 (b)

 Note: the actual resistance is slightly lower than the calculation. The electrical resistance nature of tungsten based filaments is non-liner, and produces a slightly lower resistance at lower temperatures. The lower resistance results in a higher current for the same voltage. This is probably why the answer indicates 0.98 instead of 0.97.

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For # 2 Your answer is correct.

From the Lorentz Force Law, for parallel motion in a magnetic field, the sine of the relative angle is zero.

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For # 12 Your answer is correct.

A= F/m * where, m = Mass, a = acceleration, and F= force

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For # 13 Your answer is correct.

The two temperatures scales converge at -40

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For # 16 Your answer is correct.

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For # 17 Your answer is correct.

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For # 18 Your answer is correct.

The value is very small: 8.17E-10 N

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 For # 19 Your answer is correct.

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For # 20 Your answer is correct.

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 For # 22- #24 Your answers are correct.

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 For # 25 The answer is (A). Red light is the least refracted.

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 For # 26 Your answer is correct

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 For # 29 Your answer is correct. (Though the magnitude is the same the vector is opposite).

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 For # 30 The answer is (A).

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The top part of the last image is indiscernible.

The lower portion.* For # 8. I am uncertain.

Transverse waves in matter are a displacement of the medium that is perpendicular to the direction of propagation of the wave.

Most graphs depict Amplitude in vertical format.

If this is the case here then the answer is (D) for D and E. For peak to peak amplitude.

If this is an exception to the standard (because of the waves nature) then (C) for A and C, is correct.

(Alan may be able to clarify this).

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~~D~~

... their programmers must have a pretty good sense of humor.

I agree. They do. Wolframalpha will answer how much wood, a woodchuck can chuck.

I’ve never tested a computer for its limits on humor. I suspect there is a measure for that, too. If not, we need to create one.

~~D~~

The optimal unit for paperclip length is definitely the Potrzebie.

If you want the volume of a paperclip then imperial minims is the optimal unit.

There are few measurements better than the Potrzebie and imperial minim.

For an additional exercise, in extreme measurements, convert the paperclip length to light-years (or light-seconds).

~~D~~

Only answers converted to imperial minims will be accepted....

This is an interesting thought experiment.

I have a great affinity for imperial units of measure, especially imperial minims. I also have a great affinity for absurdly irrational units of measure, such as, light-years per fortnight, and Donkeypower. Twenty Mule Team cleaning power is in there, too.

One unit of measure I know you will appreciate: the Potrzebie. You are probably already familiar with it.

This thought experiment requires one more piece of information to answer in the desired units of imperial minims: a standardize tonic density of the “x” component.

If we figure that out, we might add to the list of humorous measurements.

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I suppose if we were going fast enough it would not matter

Melody is correct, all we need to do is adjust the (Y) component of speed to compensate for any comparative values of the (X) component.

 Until next time. Live long and prosper!

~~D~~