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Consider circuit in figure. How much ene...

Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the of drift velocity ?

Text Solution

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Current in the circuit I = `(V)/(R) = (6)/(6) = 1 A `
Number density of electron n = `(10^(29))/(m^(3))`
Length of wire of circuit l = 10 cm = 0.1 m Area of cross section A = `(1 mm)^(2)`
`rArr` Current due to electron moving with drift velocity,
`I = "nAv" d^(e) `
`therefore v_(d) = (I)/("nAe") `
` = (1)/(10^(29) xx (10^(-3))^(2) xx 1.6 xx 10^(-19)) `
` = (10^(-5))/(16) (m)/(2) = 0.0625 xx 10^(-5) (m)/(s)`
` = 6.25 xx 10^(-3) (m)/(s)`
`rArr` Energy absorbed in form of K.E.,
K.E. = `(1)/(2) m_(e) v_(d)^(2) xx ` nAl
`= (1)/(2) xx 9.1 xx 10^(-31) xx (6.25 xx 10^(-3))^(2)`
`xx 10^(29) xx 10^(-6) xx 10^(-1)`
`= 177.7 xx 10^(-19)`
`therefore K.E. " " approx 1.78 xx 10^(-17) ` J
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