Cross-sectional area of silicon slab at 300 K temperature having length 10 cm is `1 xx 10^(-4) m^(2)` Find the current passing through slab if 2 V battery is joined paraUcl to its lengch mobility of electron = 0.14 `m^(2) V^(-1) S^(-1)` and electron density ` = 1.5 xx 10^(16) m^(-3)` .

Options

A. `6.72 xx 10^(-4)` A
B. `6.72 xx 10^(-5) ` A
C. `6.72 xx 10^(-6) `A
D. `6.72 xx 10^(-7)` A

Answer

D

Explanation

`6.72 xx 10^(-7)` A
l = 10 cm = `10^(-1)` m , A = 1 `xx 10^(-4) m^(2)`
V = 2 V , I = (?)
`mu = 0.14 m^(2) V^(-1) s^(-1)`
n = 1.5 ` xx 10^(16) m(-3)`
Current passing through slab = I = `"nev"_(d)`A but , `mu = (v_(d))/(E) rArr v_(d)= E mu `
`therefore I = " ne E "mu A `
Here V = El `rArr E = (V)/(l) `
`therefore I = ("neV"mu A)/(l) `
` = (1.5 xx 10^(16) xx 1.6 xx 10^(-19) xx 0.14xx 2 xx 10^(-4))/(10^(-1))`
`therefore I = 6.72 xx 10^(-7)` A