Question

A current of 3.6 mA is flowing through the element of a vacuum tube. How many electrons are flowing per second through the element? How much charge will páss in 10 minutes? Given that the magnitude of charge on each electron is 1.6 × 10^-19 C.​

Answer 1

Given :

• Current, I = 3.6 mA
• Charge of electron, e = $\sf 1.6\times 10^{-19}C$

To Find :

• Number of electrons flowing per second through the element, n = ?
• How much charge will páss in 10 minutes, Q = ?

Solution :

As, we have :

• Current, I = 3.6 mA = $\sf 3.6 \times 10^{-3} A$
• Charge of electron, e = $\sf 1.6\times 10^{-19}C$

So, to find number of electrons flowing per second through the element, we know that :

$\bull \: \: \: \: \underline{ \boxed{ \pink{\bf I = \dfrac{ne}{t} } }} \: \pink{\dag}$

By substituting values :

$\sf : \implies 3.6 \times 10^{-3} A = \dfrac{n \times 1.6\times 10^{-19}C}{1 \: s} \\\sf : \implies 3.6 \times 10^{-3} A = n \times 1.6\times 10^{-19}C \\\sf : \implies n = \dfrac{3.6 \times 10^{-3} A }{1.6\times 10^{-19}C } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\sf : \implies n = \dfrac{3.6 \times 10^{19} }{1.6\times 10^{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\sf : \implies n = \dfrac{3.6 \times 10^{16} }{1.6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\\sf : \implies n = 2.25 \times 10^{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\underline{ \tt Hence, \: number\: of\: electrons\: flowing\: per\: second\: through\: the\: element = \pink{ \bf 2.25 \times 10^{16}}}$

Now, to find total amount of charge flown in 10 minutes(10 × 60 = 600s), we know that :

$\bull \: \: \: \: \underline{ \boxed{ \pink{\bf Q = It } }} \: \pink{\dag}$

By substituting values :

$\sf : \implies Q = 3.6 \times 10^{-3} A \times 600s \\ \sf : \implies Q =2.16C \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\underline{ \tt Hence, \: total\: amount \: of\: charge\: flowing\: per\: 10 \: minutes\: through\: the\: element = \pink{ \bf 2.16C}}$