Question

A potential difference of $2V$ is applied between the opposite faces of a $Ge$ crystal plate of area $1c{m}^2$ and thickness $0.5mm$. If the concentration of electrons in $Ge$ is $2\times 10^{19}/m^2$ and mobilities of electrons and holes are $0.36m^2{V}^{-1}{s}^{-1}$ and $0.14m^2{V}^{-1}{s}^{-1}$ respectively, then the current flowing through the plate will be

• A. 0.25 A
• B. 0.45 A
• C. 0.56 A
• D. 0.64 A

Answer 1

Answer: (D)

Conductivity, $\sigma =ne\left({\mu }_e+{\mu }_h\right)$
$=2\times 10^{19}\times 1.6\times 10^{-19}$
$(0.36+0.14)=1.6(\Omega m{)}^{-1}$
$R=\rho \frac{l}{A}=\frac{l}{\sigma A}$
$=\frac{0.5\times 10^{-3}}{1.6\times 10^{-4}}=\frac{25}{8}\Omega$
$i=\frac{V}{R}=\frac{2}{25/8}$
$=\frac{16}{25}A=0.64A$