# A copper wire has

Given:

r =

Area of the cross-section can be calculated by,

The Resistivity of the resistor,

Resistance, R= 10

Formula used:
Resistance,
Where,
ρ is the resistivity of the copper wire
L is the length of the copper wire
A is the area of the cross-section of the wire
Solving the above equation for the length

Putting the values in the above equation, we get

Thus, the length of copper wire required to make 10 resistance will be 122.5 meters.

(b)   If the diameter is twice, D'=2D
Where,
D' is the new diameter
D is the initial diameter
Then, according to the question, the new diameter is twice the initial diameter.
D' = 2(0.5mm)  = 1mm

Now, the new radius R' =D (Initial diameter of the cross-section)= D'/2 = 0.5 mm
As we know,

Putting the values in the above formula, we get

Thus, Resistance, R=2.5 Ω
Thus, if we twice the diameter of the copper wire the resistance become the quarter part of the initial resistance.

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