A 14.5
metal wire is cut into three equal
pieces that are then connected side by side to
form a new wire the length of which is equal
to one-third the original length.
What is the resistance of this new wire?
Answer in units of
.
area has been increased by three, lessens resistance by 1/3
length has been shortened by three, so resistance is cut another 1/3
1/9 original resistance.
To find the resistance of the new wire, we need to consider a few things:
1. Resistance is directly proportional to the length of the wire.
2. Resistance is inversely proportional to the cross-sectional area of the wire.
3. When wires are connected in parallel, their total resistance can be calculated using the formula: 1/RTotal = 1/R1 + 1/R2 + 1/R3 (where R1, R2, and R3 are the resistances of the individual wires).
Let's work through the problem step by step:
1. We are given that the original wire's length is 14.5 units. Since the new wire is formed by connecting three equal pieces side by side, each piece will have a length equal to 14.5/3 units.
2. We are not given any information about the cross-sectional area of the wires. Without this information, we cannot calculate the resistance accurately. Resistance depends on both length and cross-sectional area, so we need to know the size of the wire (e.g., its diameter or gauge) to calculate resistance accurately. Therefore, we cannot determine the resistance of the new wire without the cross-sectional area information.
To find the resistance of the new wire, please provide the cross-sectional area or any additional information regarding the wire's dimensions.