AP Physics 1 : Resistivity
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Example Questions
Example Question #1 : Resistivity
Consider the circuit:
The current flowing through the entire circuit is 
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?
Decreasing the cross-sectional area of the cord
Increasing the length of the cord
Increasing the cross-sectional area 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, 
Example Question #2 : Resistivity
An electrician wishes to cut a copper wire 
2.6cm
960m
38m
9.6m
10cm
960m
To relate resistance R, resistivity 
Rearranging to isolate the quantity we wish to solve for, L, gives the equation 
Plugging in our numbers gives the answer, 960m.
Example Question #2 : Resistivity
What is the current in a circuit with a 
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 #1 : Resistivity
In the circuit above, your aim is to limit the current to 
To make this resistor, you have a spool of mystery metal, which has a cross sectional area of 
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 #1 : Resistivity
What is the resistance of a 
Resistance and resistivity are related as follows:
Example Question #3 : 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 
Student B's wire should be 
Student B's wire should be twice as long as 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
Resistance is proportional to length, and inversely proportional to cross-sectional area. Area depends on the square of the radius: 
Example Question #2 : Resistivity
By how much will resistivity change if resistance and length are constant, and cross sectional area is doubled?
The resistivity will not change
The resistivity will double
The resistivity will be halved
The resistivity will be quadrupled
The resistivity will double
Recall the formula for resistance 
Solve for resistivity:
From this, we can tell that resistivity is proportional to cross sectional area by:
Since 
Example Question #1 : Resistivity
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 
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 #1 : Resistivity
What is the resistance of a copper rod with resistivity of 
The equation for resistance is as follows: 
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