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

Answer:

The conductivity of Nichrome is $2\times 10^6\ S/m$.

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:

$R=\frac{V}{A}=\frac{2.0}{4.0}=0.5\ \Omega$

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

$R=\rho\frac{L}{A}$

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

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

$0.5\ \Omega=\rho\frac{1.0\ m}{1\times 10^{-6}\ m^2}\\\\\rho=\frac{0.5\times 1\times 10^{-6}}{1.0}=0.5\times 10^{-6}\ \Omega-m$

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

$\sigma=\frac{1}{\rho}=\frac{1}{0.5\times 10^{-6}}=2\times 10^6\ S/m$

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

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