Applying the science practices: examining resistance
Using the PhET Simulation “Resistance in a Wire”, design an experiment to determine how different variables – resistivity, length, and area – affect the resistance of a resistor. For each variable, you should record your results in a table and then create a graph to determine the relationship.
Test prep for ap courses
Which of the following affect the resistivity of a wire?
Suppose the resistance of a wire is
R Ω. What will be the resistance of another wire of the same material having the same length but double the diameter?
The resistances of two wires having the same lengths and cross section areas are 3 Ω and 11 Ω. If the resistivity of the 3 Ω wire is 2.65 × 10
−8 Ω∙m, find the resistivity of the 1 Ω wire.
Suppose the resistance of a wire is 2 Ω. If the wire is stretched to three times its length, what will be its resistance? Assume that the volume does not change.
The resistance
of a cylinder of length
and cross-sectional area
is
, where
is the resistivity of the material.
Values of
in
[link] show that materials fall into three groups—
conductors, semiconductors, and insulators .
Temperature affects resistivity; for relatively small temperature changes
, resistivity is
, where
is the original resistivity and
is the temperature coefficient of resistivity.
[link] gives values for
, the temperature coefficient of resistivity.
The resistance
of an object also varies with temperature:
, where
is the original resistance, and
is the resistance after the temperature change.
Conceptual questions
In which of the three semiconducting materials listed in
[link] do impurities supply free charges? (Hint: Examine the range of resistivity for each and determine whether the pure semiconductor has the higher or lower conductivity.)
Does the resistance of an object depend on the path current takes through it? Consider, for example, a rectangular bar—is its resistance the same along its length as across its width? (See
[link] .)
Explain why
for the temperature variation of the resistance
of an object is not as accurate as
, which gives the temperature variation of resistivity
.
What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when
is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)
(a) To what temperature must you raise a copper wire, originally at
,
to double its resistance, neglecting any changes in dimensions? (b) Does this happen in household wiring under ordinary circumstances?
A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at
. Over what temperature range can it be used?
An electronic device designed to operate at any temperature in the range from
contains pure carbon resistors. By what factor does their resistance increase over this range?
(a) Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has
) when it is at the same temperature as the patient. What is a patient's temperature if the thermistor's resistance at that temperature is 82.0% of its value at
(normal body temperature)? (b) The negative value
for
may not be maintained for very low temperatures. Discuss why and whether this is the case here. (Hint: Resistance can't become negative.)
(a) Redo
[link] taking into account the thermal expansion of the tungsten filament. You may assume a thermal expansion coefficient of
. (b) By what percentage does your answer differ from that in the example?
(a) To what temperature must you raise a resistor made of constantan to double its resistance, assuming a constant temperature coefficient of resistivity? (b) To cut it in half? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable, or which premises are inconsistent?
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?