Question

if I is the current flowing through a conductor for time t and e be the charge of electron, then the number of electrons transferred is. ​

Answer 1

Given :-

Current flowing = I

Time = t

Charge of electron = e

As we know that Current is the rate of flow of charge.

I = Q/t

Q = It ------(1)

We also know that,

Q = ne -----(2)

Here, n = number of electrons

e = Charge on electron

Putting (2) in (1).

ne = It

n = It/e

Hence,

Number of electron transferred = n = It/e

Answer 2

Given that , The flowing current through the conductor is ' I ' , Time is the ' t ' & the Charge of Electron is ' e ' .

Need To Find : Number of ( e ) transferred ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━⠀

⠀⠀▪︎⠀We know that , if a Charge ( Q ) flows through the cross section of Conductor in Time ( t ) then it is know as Current ( I ) and in Mathematical expression it's Given by ,

$\qquad:\implies \sf \: I \: ( \:or \: Current \:) \:= \: \dfrac{ Q }{t} \:\\\\\qquad:\implies \sf \: I \: \:= \: \dfrac{ Q }{t} \:\\\\\qquad:\implies \sf \: Q \:= \: I\:t \:$

$\qquad \therefore \pmb{\sf Q \: =\: I \: t \: \qquad \bigg\lgroup \sf{ \:Equation \:\: 1 \:}\bigg\rgroup}$

⠀⠀⠀⠀⠀⠀Here , Q is the Electrical charge , I is the Current flowing through Conductor & t is the time taken.

⠀⠀⠀AND ,

⠀⠀▪︎⠀We know that , The total number of electrons ( n ) multiplied by the charge on 1 electron ( e ) it is known as Electric Charge ( Q ) and in Mathematical Expression it's Given by ,

$\qquad:\implies \sf \: Q \: ( \:or \:Charge \:) \:=\: n \:e \:\\\\\qquad:\implies \sf \: Q \:=\: n \:e \:$

$\qquad \therefore \pmb{\sf Q \: =\: n \: e \: \qquad \bigg\lgroup \sf{ \:Equation \:\: 2 \:}\bigg\rgroup}$

⠀⠀⠀⠀⠀⠀Here , Q is the Electrical charge , n is the number of electrons & e is the charge on electron .

⠀⠀⠀⠀⠀⠀$\bigstar \underline {\pmb{\cal{\:Now \: By \: Substituting \: the \: Equation \: 2 \: in \:Equation \: 1\::}}}$

⠀⠀⠀⠀We get ,

$\qquad \dashrightarrow \sf n\:e\:\:=\:\: I \:t \:\\\\ \qquad \dashrightarrow \sf n\:\:\:=\:\: \dfrac{ \:I \:t\:}{e} \:$

$\qquad \therefore \pmb{\sf n \:\big( \:Transfered \:_{\:(Electrons)}\:\big)\: =\: \dfrac{\:I \:t\:}{e}}$

⠀⠀⠀⠀⠀⠀Here , n is the number of electrons , I is the Current flowing through Conductor , t is the time taken &, e is the charge on electron.

⠀⠀⠀⠀⠀⠀⠀∴ Hence , The number of Transfered electrons ( n ) is the ❝ I t / e ❞ .