**A 10 m long wire of a particular material is of reistance 5Ω What will be the resistance: (i) … iv) if the wire is stretched to…**

###### Answers:

**Given : **The resistance of 10m long wire = 5Ω

**(i)** R α *l* for same thickness material so if the length of wire becomes half of previous value, resistance will also become 1/2th of its previous value.

Or R = ½ x 5Ω = 2.5Ω

**(ii) **For the wire of double the radius, the area of cross-section (a = πr^{2}) of wire will be four times that of previous wire. Since resistance R α 1/a. So the resistance of new –wire will be one-fourth of the previous wire, i.e., it will be ¼ x 5Ω = 1.25Ω

**(iii) **On doubling the wire on itself the length is reduced to half and area of cross section is doubled so the resitance is reduced to one-fourth i.e., the resistance of the wire will become :

¼ x 5Ω = 1.25Ω

**(iv)** On stretching the wire to double its length, the length is doubled and its area of cross-section is reduced to half. So the resistance becomes four ‘times’ i.e., the resistance of the wire will become :

4 x 5Ω = 20Ω