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).
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:
(view answer)