# High School Physics : Resistivity

## Example Questions

### Example Question #2 : Resistivity

Ten resistors, each with resistance, are set up in series. What is their equivalent resistance?      Explanation:

For resistors aligned in series, the equivalent resistance is the sum of the individual resistances. Since all the resistors in this problem are equal, we can simplify with multiplication.  ### Example Question #3 : Resistivity

What is the total resistance of a parallel circuit with resistors of , , and ?      Explanation:

The formula for resistance in parallel is: We are given the values for each individual resistor, allowing us to solve for the total resistance.   ### Example Question #5 : Resistivity

An electric circuit is set up in series with five resistors. If the resistors remain the same, but the circuit is now set up with the resistors in parallel, how would this affect the total resistance?

Resistance would remain unchanged

We need to know the numerical values to solve

Resistance would increase substantially

Resistance would decrease substantially

Resistance would decrease substantially

Explanation:

Think of resistors as doors, preventing the flow of people (electrons). Imagine the following scenarios: a large group of people are in a room and all try to leave at once. If the five resistors are in series, that's like having all of these people trying to go through all five doors before they can leave. In a circuit, all the electrons in the current mast pass through every resistor.

If the resistors are in parallel, it's like having five separate doors from the room. All of a sudden, the group can leave MUCH faster, encountering less resistance to their flow out of the room. The path of the electrons can split, allowing each particle to pass through only one resistor.

From a formula perspective, the resistors in series are simply summed together to find the equivalent resistance. In parallel, however, the reciprocals are summed to find the reciprocal equivalent resistance. Adding whole numbers will always give you a much greater result than adding fractions. For the exact same set of resistors, arrangement in series will have a greater total resistance than arrangement in parallel.

### Example Question #6 : Resistivity

When current in a circuit crosses a resistor, energy is lost. What form does this lost energy most commonly take?

The energy is converted into sound

The energy is converted into heat

The energy is converted into light

The energy is not converted; it simply disappears

The energy is converted into motion

The energy is converted into heat

Explanation:

In basic resistors, energy lost due to resistance is converted into heat. In some cases, other conversions also take place (such as generation of light in a lightbulb), but heat is still dissipated along with any alternative conversations. Lightbulbs, batteries, and other types of resistors will become hot as current passes through them.

### Example Question #7 : Resistivity

You have a long, diameter copper wire that has an electric current running through it. Which of the following would decrease the wire's overall resistivity?

Decreasing the length of the wire

Increasing the diameter of the wire

Increasing the length of the wire

Decreasing the diameter of the wire

None of these

None of these

Explanation:

The formula for resistance is: Above, is length, is the cross-sectional area of the wire, and is the resistivity of the material, and is a property of that material. The resistivity is constant for a given material, and thus cannot be changed by altering the dimensions of the wire.

### Example Question #8 : Resistivity

Two aluminum wires have the same resistance.  If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire?      Explanation: The area of a wire is the area of a circle.  So let’s substitute that into our equation   This can be simplified to Since we know that both resistors have the same resistivity and the same resistance, we can set these equations equal to each other. Many things fallout which leaves us with We know that the second wire is twice the length as the first So we can substitute this into our equation The length of the wire drops out of the equation Now we can solve for the diameter of the longer wire. Take the square root of both sides Therefore the ratio of the long to the short wire is Or ### Example Question #1 : Resistivity

What is the diameter of a length of tungsten wire whose resistance is ohms?      Explanation:

We will use the resistivity equation to solve for this.  We know

Length = Resistance = ρ of Tungsten = The equation for resistivity is We can rearrange this equation to solve for  In this case the area of the wire is the area of a circle which is equal to We can rearrange this to get the radius by itself   To find the diameter we need to multiply this value by 2. ### Example Question #1 : Resistivity

The resistivity of most common metals __________________ .

increases as the temperature increases

varies randomly as the temperature increases

remains constant over wide temperature ranges

decreases as the temperature increases 