Question

A block of pure silicon at $300\, K$ has a length of $10\, cm$ and an area of $1.0\, cm^2$. A battery of emf $2\, V$ is connected across it. The mobility of electrons is $0.14 \,m^2 \,V^{-1}\, s^{-1}$ and their number density is $1.5 \times 10^{16}\, m^{-3}$. The electron current is

• A. $6.72 \times 10 ^{-4}\, A$
• B. $6.72 \times 10^{-5}\, A$
• C. $6.72 \times 10^{-6}\, A$
• D. $6.72 \times 10^{-7}\, A$

Answer 1

Answer: (D)

As $E = \frac{V}{l} = \frac{2V}{0.1 m}$
$= 20 \,V m^{-1}$
$ A = 1.0 \,cm^{2} $
$ = 1.0 \times 10^{-4}m^{2} $
$ v_{e} = \mu_{e} E $
$= 0.14 \times 20 $
$= 2.8 ms^{-1} $
The electron current is
$ I_{e} = n_{e}Aev_{e} $
$ = \left(1.5\times 10^{16}\right)\times \left(1.0\times 10^{-4}\right) \times \left(1.6\times 10^{-19}\right)\times 2.8 $
$ = 6.72\times 10^{-7} A$