Question

Calculate the specific resistance of the material of a cable 15m long having resistance 2Ω and cross sectional area 2 X 10-6.​

Answer 1

Answer:

Given : R=2Ω l=1 m d=0.4 mm =0.0004 m

Cross section area of wire A=

4

πd

2

=

4

π×(0.0004)

2

=1.256×10

−7

m

2

Resistivity of the material ρ=

l

RA

∴ ρ=

1

2×1.256×10

−7

=2.514×10

−7

Ωm

Answer 2

Given :

Length (L) = 15 m

Resistance (R) = 2 Ω

Cross-sectional area (A) = 2×$10^{-6}$ m²

To Find :

The specific resistance (S) of the material of a cable

Solution :

The formula for resistance is $\frac{S * L}{A}$

Where, L = Length; S = Specific Resistance; A = Area of cross-section

∴ Resistance of the cable =        $\frac{S * L}{A}$

⇒                2                      =        $\frac{S * 15}{2 * 10^{-6} }$

⇒                         4 × $10^{-6}$  =        15×S

∴                                  S     =   0.267 × $10^{-6}$ Ωm      

Therefore, The specific resistance of the material of a cable is 0.267 × $10^{-6}$ Ωm.