the resistance of a certain length wire having diameter 5mm is 10 omega if the diameter is change to 10 mm the new resistance in omega is
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To calculate the new resistance of a wire when the diameter is changed, we can use the formula for resistance:
R = ρ * (L / A)
Where:
R = Resistance
ρ = Resistivity of the wire material
L = Length of the wire
A = Cross-sectional area of the wire
In this case, we have the initial resistance (R1 = 10 Ω) and initial diameter (d1 = 5 mm), and we want to find the new resistance (R2) when the diameter is changed to 10 mm.
To proceed, we need to find the initial cross-sectional area (A1) and the new cross-sectional area (A2). The cross-sectional area of a wire can be calculated using the formula:
A = π * (d^2 / 4)
Let's calculate the initial and new cross-sectional areas:
For the initial diameter (d1 = 5 mm):
A1 = π * (5 mm)^2 / 4
And for the new diameter (d2 = 10 mm):
A2 = π * (10 mm)^2 / 4
Now, we can rearrange the resistance formula to solve for the new resistance (R2):
R2 = R1 * (A1 / A2)
Substituting the initial resistance (R1 = 10 Ω) and the calculated cross-sectional areas (A1 and A2), we can find the new resistance (R2).