A potential difference of 2 V is applied between the opposite faces of a Ge crystal plate of area 1cm2 and thickness 0.5 mm. If the concentration of electrons in Ge is 2×1019/m3 and mobilities of electrons and holes are 0.36m2volt-sec and 0.14m2vol−sec respectively, then the current flowing through the plate will be n. Then the value of n×100 is (in A)

σ=ne(μe+μh)=2×1019×1.6×10−19(0.36+0.14)=1.6(Ω−m)−1 R=ρlA=lσA=0.5×10−31.6×10−4=258Ω∴ i=VR=225/8=1625A=0.64A

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A potential difference of 2 V is applied between the opposite faces of a Ge crystal plate of area $1 c m^{2}$ and thickness 0.5 mm. If the concentration of electrons in Ge is $2 \times 10^{19} / m^{3}$ and mobilities of electrons and holes are $0.36 \frac{m^{2}}{volt-sec}$ and $0.14 \frac{m^{2}}{vol - \sec}$ respectively, then the current flowing through the plate will be $n$ . Then the value of $n \times 100$ is (in A)

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answer is 64.

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Detailed Solution

$σ = n e (μ_{e} + μ_{h}) = 2 \times 10^{19} \times 1.6 \times 10^{- 19} (0.36 + 0.14) = 1.6 {(Ω - m)}^{- 1} \begin{array}{l} R = ρ \frac{l}{A} = \frac{l}{σ A} = \frac{0.5 \times 10^{- 3}}{1.6 \times 10^{- 4}} = \frac{25}{8} Ω \\ ∴ i = \frac{V}{R} = \frac{2}{25 / 8} = \frac{16}{25} A = 0.64 A \end{array}$