Question

A potential difference of $2\text{V}$ is applied across the opposite faces of a Germanium plate, of area $1{\text{cm}}^2$ and thickness $0.5\text{mm}$. If the concentration of electrons is $2\times {10}^{19}{\text{m}}^{-3}$ and mobilities of electrons and holes are $0.36{\text{m}}^2\text{/V-s}$ and $0.14{\text{m}}^2\text{/V-s}$ respectively, the current flowing through the plate will be,

• A. $0.24\text{A}$
• B. $0.32\text{A}$
• C. $0.48\text{A}$
• D. $0.64\text{A}$

Answer 1

The correct option is D $0.64\text{A}$

Conductivity of Germanium is given by,

$\sigma =n{q}_e({\mu }_e+{\mu }_h)$

$=2\times {10}^{19}\times 1.6\times {10}^{-19}(0.36+0.14)$

$=1.6{(\Omega -\text{m})}^{-1}$

Now, $R=\rho \frac{l}{A}=\frac{l}{\sigma A}$

$R=\frac{0.5\times {10}^{-3}}{1.6\times {10}^{-4}}=\frac{25}{8}\Omega$

And, $I=\frac{V}{R}=\frac{2}{\frac{25}{8}}=0.64\text{A}$

Hence, $\left(D\right)$ is the correct answer.