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Question: How many electrons constitute current of one microampere in one second? \(\begin{aligned} & \te...

How many electrons constitute current of one microampere in one second?
A. 6.25 × 108 B. 6.25 × 1012 C. 6.25 × 109 D. 6.25 × 1015 \begin{aligned} & \text{A}\text{. }6.25\text{ }\times \text{ 1}{{\text{0}}^{8}} \\\ & \text{B}\text{. 6}\text{.25 }\times \text{ 1}{{\text{0}}^{12}} \\\ & \text{C}\text{. 6}\text{.25 }\times \text{ 1}{{\text{0}}^{9}} \\\ & \text{D}\text{. 6}\text{.25 }\times \text{ 1}{{\text{0}}^{15}} \\\ \end{aligned}

Explanation

Solution

In per unit time, the amount of charge which flows through a conductor is known as electric current. The SI unit of the current is ampere. According to the Coulomb's Law, the electric current is equal to the ratio of charge and time i.e. Q/T.

Complete step by step answer:
-In the given question, we have to calculate the no. of the electron which will be required to carry a current of 1 microampere in one second.
-Also, we know that an electron carries a negative charge and they can move through which they can conduct electricity.
-Now, according to the definition of the electric current, the formula of electric current is: I = QT\text{I = }\dfrac{\text{Q}}{T}
Where Q is the charge which is also equal to the product of no. of electrons and electronic charge (ne) and T is the time in seconds.
So, I = QT = neT\text{I = }\dfrac{\text{Q}}{T}\text{ = }\dfrac{\text{ne}}{T}
-Now, the value of e is always fixed i.e. 1.6 × 10−19C\text{1}\text{.6 }\times \text{ 1}{{\text{0}}^{-19}}\text{C}.

-it is given that time T is 1 second and current I is 1 ampere. So, the number of electrons will be:
n = ITe = 1 × 11.6 × 10−19\text{n = }\dfrac{\text{IT}}{e}\ \text{= }\dfrac{1\text{ }\times \text{ 1}}{1.6\text{ }\times \text{ 1}{{\text{0}}^{-19}}} = 6.25 × 10−19=\ \text{6}\text{.25 }\times \text{ 1}{{\text{0}}^{-19}}electrons

-So, 6.25 × 10−19\text{6}\text{.25 }\times \text{ 1}{{\text{0}}^{-19}} electrons will be required to carry the current of 1 microampere in one second.
So, the correct answer is “Option B”.

Note: Electrons are responsible for the conduction of electricity because of their movement because they are negatively charged particles so when they move towards positive charge in the presence of electric field they conduct or produce electricity.