Find the current produces at room temperature in pure germanium rod of area $4 \times 10^{- 4} m^{2}$ and thickness $2.4 \times 10^{- 3} m .$ When the potential of 5V is applied across the faces. The concentration of charge carriers with germanium at room temperature at $3.2 \times 10^{6} p e r c u b i c m e t r e .$ The mobility of electron and hole are $0.8 m^{2} v^{- 1} s^{- 1} a n d 0.4 m^{2} v^{- 1} s^{- 1}$ respectively.

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$1.28 \times 10^{- 13} A$

$2.56 \times 10^{- 13} A$

$5.12 \times 10^{- 13} A$

$9.4 \times 10^{- 13} A$

answer is C.

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Detailed Solution

$\begin{array}{l} C o n d u c t i v i t y, σ = n_{i} e (μ_{e} + μ_{h}) \\ \Rightarrow σ = 3.2 \times 10^{6} \times 1.6 \times 10^{- 19} [0.8 + 0.4] = 6.144 \times 10^{- 13} \\ C u r r e n t, i = J A = σ E A = σ (\frac{V}{d}) A = 6.144 \times 10^{- 13} \times \frac{5}{24 \times 10^{- 4}} \times 4 \times 10^{- 4} \\ \Rightarrow i = 5.12 \times 10^{- 13} A \end{array}$