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Question:

A copper wire has a diameter 0.5 mm and resistivity of 1.6 × 10^{–8} Ω m. What will be the length of this wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?

Answer:

Given:

Diameter,

Radius,

Resistivity,

Resistance,

Length of wire,

We know,

Here, the area of cross section

Putting this value in (1)

Again using,

The new resistance when the diameter is double is given by,

Dividing (3) by (2)

So, the decrease in the resistance

Decrease in the resistance

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