Question

A 1.5 m length of wire has a cross-sectional area of 5.0×10−8 m2. When the potential difference across its ends is 0.20 V, it carries a current of 0.40 A. What is the resistivity of the material from which the wire is made?

Answer 1

Given that ,

L = 1.5 m

A = 5 × 10 -8  m 2

V = 0.20 V

I = 0.40 A

By ohms law

I = V/R ........(1)

I = current flowing through the conductor

V = potential difference between the ends of the conductor

R = resistance of the conductor

For a given conductor

R = l /A

= resistivity of the conductor

l = length of the conductor

A = area of cross section of the conductor

Substituting the value of R in (1)

I = V/ (l / A)

I = V A / l

= V A/ I l

= (0.2 × 5 × 10 -8 ) / (0.40 × 1.5 )

= 1.667 × 10 - 8 m

The resistivity of the wire = 1.667 × 10 -8 m