Page 25 - CHAPTER-1 (Electricity)

CHAPTER 1

ELECTRICITY

Example 7:

A wire of an unknown material having length and area of cross-

section A has a resistance of 10Ω. What will be the resistance of a similar

wire with the same material having length /4 and area of cross section

2.5A?

Solution: For first wire, length = , area of cross section = and

resistance, R =10Ω
1

l
R = ρ = 10Ω ⟹ ρ= 10A
1
l
A
For second wire, length = /4, area of cross-section =2.5A

l
l
4
∴ Resistance, R =ρ 2.5A = 10A . 4×2.5A =1Ω
2
l
So, the resistance of that wire is 1Ω.

Example 8:

The resistance of an unknown metal wire having a length 2m is 30Ω at

temperature 25 . If we are given that the diameter of the wire is
0

0.6mm, then find the resistivity of the metal at the given temperature?

Solution:

Given, length of wire, l=2m

-4
Diameter of wire, d=0.6mm=6×10 m

The resistivity of the wire, ρ= ? We know that,

-4
RA Rπd 2 30×π×(6×10 ) 2
-6
ρ = = = = 4.24×10 Ω-m
l 4l 4×2

-6
The resistivity of the metal at 25 is 4.24×10 Ω-m.
0

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