Q34 of 72 Page 12

A piece of wire is redrawn by pulling it until its length is doubled. Compare the new resistance with the original value?

Let the original dimensions of the wire be of length l, area of cross section A and resistivity ρ . 
Therefore resistance R =
Since the total volume of the cylindrical wire is constant, the length of the wire is doubled by pulling it and hence the cross sectional area of the wire is halved.
Therefore the new resistance R′ = = 4R
Thus the resistance is 4 times its original value.

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32 Explain the following:
(i)  Why is tungsten used almost exclusively as filament for incandescent lamps?
(ii) Why are the conductors of electric heating devices, such as toasters and electric irons, made of an alloy rather than a pure metal?
(iii) Why is the series arrangement not used for domestic circuits?
(iv) How does the resistance of a wire vary with its cross-sectional area? 33 A piece of wire having resistance, R is cut into four equal parts. 
(i)  How will the resistance of each part compare with the original resistance?
(ii) If the four parts are placed in parallel, how will the resistance of the combination compare with the resistance of the original wire? 35 A copper wire has a diameter of 0.5 mm and resistivity of 1.6 ohm cm. How much of this wire would be required to make a 10 ohm coil? 36 Draw a schematic diagram of a circuit consisting of a battery of four 2 V cells, a 5 ohm resistor,  an 8 ohm resistor and a 12 ohm resistor and a plug key all connected in series.