Question

A bar of silicon is 4 cm long with a circular cross section. If the resistance of the bar is 280 Ω at room temperature, what is the cross-sectional radius of the bar?

Answer 1

Answer:

r = 17.05 cm

Explanation:

Given that,

Length of silicon bar is 4 cm or 0.04 m

Resistance of the bar is 280 ohms

We know that the resistivity of the silicon is 640 Ωm

We need to find the cross-sectional radius of the bar. Let it is r.

Using definition of resistance of an object. It is given by :

$R=\rho\dfrac{l}{A}$

A is area of bar, A = πr²

So,

$R=\rho\dfrac{l}{\pi r^2}\\\\r^2=\dfrac{\rho l}{R\pi}\\\\r^2=\dfrac{640\times 0.04}{280\pi}\\\\r=0.1705\ m\\\\r=17.05\ cm$

So, the cross-sectional radius of the bar is 17.05 cm.