Question

A wire of Nichrome (a nickel– chromium– iron alloy commonly used in heating elements) is 1.0 m long and 1.0 mm² in cross-sectional area. It carries a current of 4.0 A when a 2.0 V potential difference is applied between its ends. Calculate the conductivity σ of Nichrome.

Answer 1

The conductivity of Nichrome is
`2* 10^6\ S/m`.

Step-by-step explanation:

Given:

Potential difference (V) = 2.0 V

Current flowing (I) = 4.0 A

Length of wire (L) = 1.0 m

Area of cross section of wire (A) = 1.0 mm² = 1 × 10⁻⁶ m² [1 mm² = 10⁻⁶ m²]

We know, from Ohm's law, that the ratio of voltage and current is always a constant and equal to the resistance of the resistor. Therefore, the resistance of the nichrome wire is given as:

`R=(V)/(A)=(2.0)/(4.0)=0.5\ \Omega`

Now, resistance of the nichrome wire in terms of its resistivity, length and area of cross section is given as:

`R=\rho(L)/(A)`

Where,
`\rho\to resistivity\ of\ Nichrome`

Now, plug in all the values given and solve for
`\rho`. This gives,

`0.5\ \Omega=\rho(1.0\ m)/(1* 10^(-6)\ m^2)\\\\\rho=(0.5* 1* 10^(-6))/(1.0)=0.5* 10^(-6)\ \Omega-m`

Now, conductivity of a material is the reciprocal of its resistivity. Therefore, the conductivity of Nichrome is given as:

`\sigma=(1)/(\rho)=(1)/(0.5* 10^(-6))=2* 10^6\ S/m`

Conductivity is measured in Siemens per meter (S/m)

Therefore, the conductivity of Nichrome is
`2* 10^6\ S/m`.