A certain piece of wire has a resistance of 250 ohms. if the wire is cut in three pieces and the cross sectional area of each piece is halved, what is the resistance of each piece?
area halving will double resistance,cutting it into thirds reduces R.
New R= 2/3 *250
To find the resistance of each piece, we need to understand the relationship between resistance, length, and cross-sectional area of a wire.
The resistance of a wire is given by the formula:
Resistance (R) = Resistivity (ρ) * (Length (L) / Cross-sectional Area (A))
From the question, we know that the wire initially has a resistance of 250 ohms. Let's assume the length of the wire remains constant while the cross-sectional area changes.
The resistance of the wire can be expressed as:
250 = ρ * (L / A)
Now, when the wire is cut into three equal pieces, the total length of the wire remains the same, but the cross-sectional area of each piece is halved.
Let's represent the original cross-sectional area as A, and the new cross-sectional area for each piece as (A / 2).
The resistance for each piece can now be calculated using the new cross-sectional area:
Resistance (R') = ρ * (L / (A / 2))
Simplifying this equation:
R' = ρ * (2L / A)
Since the original resistance (R) is equal to 250 ohms, and the new resistance (R') is what we're looking for, we can write the equation as:
250 = ρ * (2L / A)
Now, to find the resistance of each individual piece, we divide the new resistance (R') by 3 (since the wire is cut into three equal pieces):
R'' = R' / 3
Substituting the value of R' into this equation:
R'' = (250 / 3) ohms
Therefore, the resistance of each piece of wire is approximately 83.33 ohms.