The electrical resistance of a wire is directly proportional to its length. If a 3-foot long wire has a resistance of 1 ohm(s), find the resistance of a 9-foot long wire.
What is the resistance?
If it varies directly, the resistance of a 9-foot wire is 3 times the resistance of a 3-foot wire.
To find the resistance of a 9-foot long wire, we need to use the information given that the electrical resistance is directly proportional to the length of the wire.
Let's use the formula for direct variation:
Resistance = k * Length
Where k is the constant of variation.
In this case, we are given that a 3-foot long wire has a resistance of 1 ohm. We can use this information to find the value of k.
1 ohm = k * 3 feet
To solve for k, divide both sides of the equation by 3 feet:
k = 1 ohm / 3 feet
Now that we have the value of k, we can use it to find the resistance of a 9-foot long wire:
Resistance = k * Length
Resistance = (1 ohm / 3 feet) * 9 feet
Cancelling out the feet:
Resistance = 1 ohm * 3
Therefore, the resistance of a 9-foot long wire is 3 ohms.