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# A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10-8 m. What will be the length of this wire to make its resistance 10 ? How much does the resistance change if the diameter is doubled?

(a) From the given information,

Radius of wire, r = Then area of cross-section will be, Resistivity, Resistance, R= 10 And, Length, L = (To be calculated)

Now, putting these values in the formula: Thus, the length of copper wire required to make 10 resistance will be 122.5 meters.

(b) The resistance of a wire is inversely proportional to the square of its diameter. So, when the diameter of the wire is doubled (that is, made 2 times), then its resistance will become (one-fourth).

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The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below:

I (amperes): 0.5 1.0 2.0 3.0 4.0

V (volts): 1.6 3.4 6.7 10. 2 13.2

Plot a graph between V and I plotted by using the given data is shown below: