Q33 of 72 Page 12

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?

(i) Since the resistance R is cut into 4 equal parts each part has 1/4th of the total length. Thus the resistance is 1/4th the original resistance i.e. each has a resistance of R/4. This is because R is proportional to the length of the wire.
(ii) When the 4 resistances of resistance R/4 each are connected in parallel the equivalent resistance of the circuit is R/16, i.e. it is 1/16th of the original resistance R.

More from this chapter

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31 Read the following statements. Write true or false against each:
(i)   The quantity of charge flowing past a point multiplied by the time gives the current.
(ii)  The flow of charge through a conducting wire, connected to a cell, is due to the chemical reaction inside the cell.
(iii) The resistivity of all pure metals increases with rise in temperature.
(iv) Ohm's law is a relation between the power used, the current and the potential difference in a circuit.
(v)  A series circuit has only one conducting path for the electrons that move through it; a parallel circuit has multiple conducting paths.
(vi) A conducting wire offers resistance to the flow of electrons because electrons repel each other in the wire. 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? 34 A piece of wire is redrawn by pulling it until its length is doubled. Compare the new resistance with the original value? 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?