Question

How much time 10²⁰ electrons will take to flow through a point, so that the current is 200 mA? (e = 1.6 × 10⁻¹⁹ C)

Answer 1

Given conditions ⇒

Number of the Electrons(n)  = 10²⁰ Electrons.
Charge on one Electron(e) = 1.6 × 10⁻¹⁹ C.

∴ Total charge on the Electrons(Q) = 10²⁰ × 1.6 × 10⁻¹⁹
     = 160 C.

Current = 200 mA.
 = 200 × 10⁻³ A.

Now, Using the Formula,
 Current = Charge/Time.
∴ Time = 160/200 × 10⁻³
   = 0.8 × 10³ s.
   = 8 × 10²
   = 800 s.


Hence, the time required is 8 × 10² or 800 seconds.

Answer 2

Hey There!!


Here, first have to understand that electron are charge carriers. Each electron has a charge, denoted as e.


Also, we have to understand the definition of Electric Current:


Amount of charge flowing per unit time is electric current. 


So, $I=\frac{Q}{t}$

________________________________


Let us come to the question:


We have been given that there are $10^{20}$ electrons, and each electron carries a charge of $e=1.6\times 10^{-19}\, C$



So, total charge is:


$Q=\text{No. of electrons} \times \text{Charge on each electron} \\ \\ \\ \implies Q = 10^{20} \times 1.6 \times 10^{-19} \\ \\ \\ \implies Q=1.6 \times 10 \\ \\ \\ \implies Q = 16 \, \, C$



Now, we are given that the current is 200 mA. So, 

$I =200 \, \, mA \\ \\ \implies I = 200 \times 10^{-3} \, \, A \\ \\ \implies I=0.2 \, \, A$


Now, let the time be t. 


From the mathematical form of current we know:


$I=\frac{Q}{t} \\ \\ \\ \implies t= \frac{Q}{I} \\ \\ \\ \implies t = \frac{16}{0.2} \\ \\ \\ \implies \fbox{t=800 \, \, s}$




Thus, the electrons have to flow for 800 seconds for the current to be 200 mA.



Hope it helps

Purva

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