Q191
General SciencePhysics
Resistance of a uniform metal wire of length 1 m and cross-sectional area $1\ \mathrm{cm^2}$ is $10\ \Omega$. Resistivity of the wire is
- a.$\frac{1}{10}\ \Omega$ cm
- b.$1\ \Omega$ cm
- c.$10\ \Omega$ cm
- d.$100\ \Omega$ cm
Answer: (A) $\frac{1}{10}\ \Omega$ cm
Resistance $R = \rho \frac{L}{A}$, so resistivity $\rho = \frac{RA}{L}$. Working in centimetres, $L = 1$ m $= 100$ cm and $A = 1\ \mathrm{cm^2}$: $\rho = \frac{10 \times 1}{100} = \frac{1}{10}\ \Omega$ cm. The trap is to forget the conversion of 1 m into 100 cm, which gives $10\ \Omega$ cm (option C). In SI units the answer is $10^{-3}\ \Omega$ m. Resistivity depends only on the material and its temperature, not on the length or thickness of the wire; its reciprocal is conductivity. Silver has the lowest resistivity among metals, and alloys such as nichrome, with high resistivity, are used in heating elements.