Question

A bar of silicon is 4 cm long with a circular cross section. If the resistance of the bar is 270 ω at room temperature, what is the cross-sectional radius of the bar?

Answer 1

solution:

$consider the following data\\ length of slicon bar with circular cross section is 4cm or 0.04m\\ at room temperature resistance of the slicon bar is 270\Omega \\ represent the resistance in mathematical from\\ r=p\frac{1}{A}---1\\ where r is resistance and l is the length \\ A is cross sectional area\\ it is clear that resistivity of the silicon meterial is 6.4\times^2 \Omega.m\\ substitute 6.4\times10^2 for p,270\Omega for R and 0.04m for l i equation (1).$$270=(604\times10^2)\frac{0.04}{A}\\ rewrite the equation\\ a=(6.4\times10^2)\frac{(0.04)}{270}\\ =0.9481m^2\\ write the formula for the circular cross sectional area of silicon bar.\\ A=\pi r^2\\ substitute 0.9481 for A in the above equation\\ \pi r^2=0.9481 r^2=\frac{0.9481}{3.14},since \pi =3.14\\ 0.30194\\ further simplified\\ r^2=0.30194\\ \sqrt{0.30194}\\ \cong 0.1509m\\ \cong 150.1mm$