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?
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