Question

if 10 m long manganin wire ,0.13 cm in diameter has a resistance of 3.4 ohm find the resistivity of the material what is the conductivity of the material​

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 of the wire (L) = 10 m

Radius (R) = $\frac{0.13}{2}$ = 0.065 cm = 65 × 10⁻⁵ m

Resistance (R) = 3.4 ohm

To Find :

(a) Resistivity of the material of a wire

(b) Conductivity of the material​

Solution :

We know, Resistance (R) = Resistivity (ρ) × $\frac{Length (L) }{Area (A)}$

∴ Resistivity (ρ) =  R × $\frac{A}{L}$

                         =  3.4 × $\frac{\pi (65 * 10^-^5)^2}{10}$

                         =  3.4 × $\frac{3.14 * 65 * 65 * 10^-^1^0}{10}$

                         =  3.4 × 1326.65 × 10⁻¹⁰

                         =  4510.61 × 10⁻¹⁰

                         = 4.51 × 10⁻⁷ ohm. m

Therefore, the resistivity of the material of the wire 4.51 × 10⁻⁷ Ohm. m

(b) Conductivity (σ) = $\frac{1}{Resistivity}$

                               = $\frac{1}{4.51 * 10^-^7}$

                               = 2.22 × 10⁶ ohm⁻¹.m⁻¹

Therefore, the conductivity of the wire is 2.22 × 10⁶ ohm⁻¹.m⁻¹.