Current Definition and Electron Count
The electric current ($I$) flowing through a wire is defined as the rate of flow of electric charge. The formula relating current, charge ($Q$), and time ($t$) is:
$I = \frac{Q}{t}$
This can be rearranged to find the total charge ($Q$) that flows in time $t$:
$Q = I \times t$
Relating Charge to Electrons
The total charge ($Q$) is also related to the number of electrons ($n$) passing through the wire and the elementary charge of one electron ($e$). The formula is:
$Q = n \times e$
Calculating the Number of Electrons
To find the number of electrons ($n$), we can equate the two expressions for charge ($Q$):
$I \times t = n \times e$
Now, solve for $n$:
$n = \frac{I \times t}{e}$
Therefore, the number of electrons crossing in $t$ seconds is $\frac{It}{e}$.
Final Answer Justification
- The definition of current is $I = Q/t$.
- The total charge is $Q = n \times e$.
- Substituting $Q$ gives $I = (n \times e) / t$.
- Rearranging for $n$ yields $n = (I \times t) / e$.
- This matches option 3.
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