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A N-type silicon sample of width 4xx10^(...

A `N`-type silicon sample of width `4xx10^(-3)m`, thickness and length `6xx10^(-2)m` carriers a current of `4.8mA`, when the voltage is applied across the length of the sample. The free electron density is `10^(22)m^(-3)`

Text Solution

Verified by Experts

Here, width of sample ` b = 4 xx 10^(-3)m` ,
thickness of sample, `d = 25 xx 10^(-5)m` ,
Length, `l = 6 xx 10^(-2)m`
Current `I = 4.8mA = 4.8 xx 10^(-3)A`
Current density,
`J = I/A = I/bd = (4.8 xx 10^(-3))/((4 xx 10^(-3)) xx (25 xx 10^(-3)))`
` = 4.8 xx 10^(3)Am^(-2)`
As, `J = n e v_(d)`, So
`v_(d) = (J)/(n e) = (4.8 xx 10^(-3))/(10^(22) xx (1.6 xx 10^(-19))) = 3 ms^(-1)`
Time taken by electron to travel the length l is
`t =l/v_(d) = 6xx10^(-2)/3 = 2 xx 10^(-2)s = 0.02s`
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