All AP Physics 1 Resources
Example Questions
Example Question #1 : Resistivity
Consider the circuit:
The current flowing through the entire circuit is . What is the value of R3?
We know the voltage and total current of the circuit, so we can calculate an equivalent resistance using Ohm's law:
Now we can use the expression for condensing parallel resistors to calculate R3:
Example Question #1 : Resistivity
Which of the following factors would decrease the resistance through an electrical cord?
Increasing the cross-sectional area of the cord
Decreasing the cross-sectional area of the cord
Increasing the length of the cord
Increasing the resistivity
Increasing the cross-sectional area of the cord
The equation for resistance is given by .
From this equation, we can see the best way to decrease resistance is by increasing the cross-sectional area, , of the cord. Increasing the length,
, of the cord or the resistivity,
, will increase the resistance.
Example Question #1 : Resistivity
An electrician wishes to cut a copper wire that has no more than
of resistance. The wire has a radius of 0.725mm. Approximately what length of wire has a resistance equal to the maximum
?
960m
2.6cm
10cm
9.6m
38m
960m
To relate resistance R, resistivity , area A, and length L we use the equation
.
Rearranging to isolate the quantity we wish to solve for, L, gives the equation . We must first solve for A using the radius, 0.725mm.
Plugging in our numbers gives the answer, 960m.
Example Question #2 : Resistivity
What is the current in a circuit with a resistor followed by a
resistor that are both in parallel with a
resistor? The voltage supplied to the circuit is 5V.
Resistors in serries add according to the formula:
Resistors in parallel add according to the formula:
We can find the total equivalent resistance:
Now we can use Ohm's law to find the current:
Solve:
Example Question #3 : Resistivity
In the circuit above, your aim is to limit the current to , so you must design a resistor to serve in the place of
.
To make this resistor, you have a spool of mystery metal, which has a cross sectional area of and a resistivity of,
. What length of wire should you cut?
First, find out how much total resistance should be in the circuit in order to get the desired current:
Determine what the second resistance should be.
Find the necessary length of wire.
Example Question #4 : Resistivity
What is the resistance of a length of round copper wire with a radius of
?
Resistance and resistivity are related as follows:
Example Question #1 : Resistivity
Two students are performing a lab using lengths of wire as resistors. The two students have wires made of the exact same material, but Student B has a wire the has twice the radius of Student A's wire. If Student B wants his wire to have the same resistance as Student A's wire, how should Student B's wire length compare to Student A's wire?
Student B's wire should be the same length as Student A's wire
Student B's wire should be twice as long as Student A's wire
Student B's wire should be the length of Student A's wire
Student B's wire should be the length of Student A's wire
Student B's wire should be four times as long as Student A's wire
Student B's wire should be the length of Student A's wire
Resistance is proportional to length, and inversely proportional to cross-sectional area. Area depends on the square of the radius: , so Student B's wire has
times the cross-sectional area of Student A's wire. In order to compensate for the increased area, Student B must make his wire
the length of Student A's wire. This can be shown mathematically using the equation for resistance:
Example Question #1 : Resistivity
By how much will resistivity change if resistance and length are constant, and cross sectional area is doubled?
The resistivity will double
The resistivity will not change
The resistivity will be quadrupled
The resistivity will be halved
The resistivity will double
Recall the formula for resistance is given by
, where
is the cross sectional area,
is resistivity, and
is length.
Solve for resistivity:
From this, we can tell that resistivity is proportional to cross sectional area by:
Since is doubled, and resistance
and length
are constant, resistivity
will also be doubled.
Example Question #1371 : Ap Physics 1
Ratio is given by:
Resistivity of first resistor: Resistivity of second resistor
What is the ratio of resistivity of 2 resistors with identical resistances and area, where the first resistor is twice the length of the second resistor?
Resistivity is given by:
, where
is the resistance,
is the area, and
is the length.
Since both have identical resistances and area, the first resistor will have half the resistivity since it has twice the length. Therefore the resistivity relation is
Example Question #8 : Resistivity
What is the resistance of a copper rod with resistivity of , diameter of
, and length of
?
The equation for resistance is as follows: . Where
is resistivity,
is the length of the wire, and
is the cross section of the wire which can be found using
.
All AP Physics 1 Resources
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