A 3.50 m length of wire with a cross sectional area of 3.14× 10-6m2 at 20°C has a resistance of 0.0625ohm .the resistivity of the wire is
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In the question, it is given that the resistance of one meter wire is 3 ohms. So the resistance of 1.5 meters of the same wire is given as
1
3×5
=15ohms.
The resistance of a resistor is given by the formula R=ρ
A
L
where ρ is the resistivity of the material the resistor is made of, l is the length of the resistor and A is the cross-sectional area.
Let the resistance of the wire is initially equal to R. R=ρ
A
L
.
When the area of cross-section of the wire is doubled and so the resistance of the wire is given as R
′
=ρ
2(A)
L
.
The new resistance is R
′
=
2
R
.
Hence, the changed resistance of the wire is 15/2=7.5 ohms.
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