Calculating Electrons in 10 Amperes Current

The question asks for the number of electrons flowing per second when the electric current is 10 amperes. We can calculate this using the definition of electric current and the elementary charge of an electron.

Fundamental Concepts

• Electric Current (I) is defined as the rate of flow of electric charge (Q) per unit time (t). The formula is: $ I = \frac{Q}{t} $
• Total Charge (Q) is related to the number of electrons (n) and the elementary charge (e) of a single electron. The formula is: $ Q = n \times e $ The elementary charge, e, is approximately $1.6 \times 10^{-19}$ Coulombs (C).

Step-by-Step Calculation

We need to find the number of electrons (n) flowing in t = 1 second when the current is I = 10 amperes.

1. Combine the formulas: Substitute the expression for Q into the formula for I: $ I = \frac{n \times e}{t} $
2. Solve for n: Rearrange the formula to find the number of electrons (n): $ n = \frac{I \times t}{e} $
3. Substitute the values: Plug in the given values: $I = 10$ A, $t = 1$ s, and $e = 1.6 \times 10^{-19}$ C. $ n = \frac{10 \text{ A} \times 1 \text{ s}}{1.6 \times 10^{-19} \text{ C}} $
4. Calculate the result: $ n = \frac{10}{1.6 \times 10^{-19}} $ $ n = \frac{10}{1.6} \times 10^{19} $ $ n = 6.25 \times 10^{19} $
5. Compare with options: The calculated value $6.25 \times 10^{19}$ is equivalent to $62.5 \times 10^{18}$. This closely matches option 4, $62.4 \times 10^{18}$. The slight difference is due to the approximation used for the elementary charge.

Therefore, approximately $62.4 \times 10^{18}$ electrons flow every second in ten amperes of current.