Question

A potential difference of $2.5$V is applied across the faces of a germanium crystal plate. The face area of the crystal is $1$ $c{m}^2$ and its thickness is $1.0$ mm. The free electron concentration in germanium is $2\times {10}^{19}{m}^{-3}$ and the electron and holes mobilities are $0.33m^2/V$ and $0.17m^2/V$ respectively. The current across the plate will be?

• A. $0.2$A
• B. $0.4$A
• C. $0.6$A
• D. $0.8$A

Answer 1

The correct option is B $0.4$A

A potential difference $=2.5V$

face area $=1{cm}^2=1\times {10}^{-4}{m}^2$

Thickness $t=1.0mm$ $=1\times {10}^{-3}m$

electron concentration in $Ge=2\times {10}^{19}{m}^{-3}$ electron and holes mobilities

${\mu }_e=0.33m^2/V$

${\mu }_p=0.17m^2/V$

respectively

Using the hall effect,

$V=\frac{{\mu }_p\times I\times A}{t}$

or, $V=\frac{Vt}{{\mu }_p\times A}=0.4A$