Question

A current of 0.2 A passes through a metal wire for 20 seconds. Calculate the number of electrons through the cross section of the wire during this time. The charge on an electron = 1.6 × 10^ -19 coulomb​

Answer 1

We know that,

$\bigstar\:\bf\orange{Q\:(Charge)\:=\:\dfrac{I\:(Current)}{t\:(Time)}\:}$

And

$\bigstar\:\bf\green{Q\:(Charge)\:=\:n\:e\:}$

Where,

• n = number of the electrons

• Q = Charge of an electron = 1.6 × ${10^{-19}}$ C

$\implies\:\bf{n\:e\:=\:\dfrac{I}{t}\:}$

$\implies\:\bf{n\:=\:\dfrac{I}{t}\:\times\:\dfrac{1}{e}\:}$

$\implies\:\bf{n\:=\:\dfrac{0.2}{20}\:\times\:\dfrac{1}{1.6\times{10^{-19}}}\:}$

$\implies\:\bf\red{n\:=\:1.6\times{10^{-21}}\:electrons}$

Answer 2

Answer:

A current of 2A passes through a wire for 20 minutes. The number of electrons that crossed the cross-section in this period is

Given

Current through the wire is I=2A

Time for which current flows through the wire is t=20min=20×60s

Let n and e be the number and charge of electrons that crossed the cross-section of wire in time t.

Now, the total charge, q(say) in the wire is

q=ne

Hence, the current flowing in time t is

I=  

t

q

​

 

I=  

t

ne

​

 

∴n=  

e

It

​

 

∴n=  

1.6×10  

−19

 

(2)(20×60)

​

 

∴n=  

1.6×10  

−19

 

2400

​

 

∴n=1500×10  

19

 

∴n=1.5×10  

22