Question

A potential difference of $2\, V$ is applied between the opposite faces of a $Ge$ crystal plate of area $1\, cm ^{2}$ and thickness $0.5 mm$. If the concentration of electrons in $Ge$ is $2 \times 10^{19} / m ^{2}$ and mobilities of electrons and holes are $0.36\, m ^{2} V ^{-1} s ^{-1}$ and $0.14\, m ^{2} V ^{-1} s ^{-1}$ 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, $\sigma=n e\left(\mu_{e}+\mu_{h}\right)$
$=2 \times 10^{19} \times 1.6 \times 10^{-19}$
$(0.36+0.14)=1.6(\Omega m )^{-1}$
$R =\rho \frac{l}{A}=\frac{l}{\sigma A}$
$=\frac{0.5 \times 10^{-3}}{1.6 \times 10^{-4}}=\frac{25}{8} \Omega$
$i =\frac{V}{R}=\frac{2}{25 / 8}$
$=\frac{16}{25} A =0.64\, A$