Step 1: Recall the formula for electric current.
Electric current (\( I \)) is defined as the rate of flow of electric charge (\( Q \)):
\[
I = \frac{Q}{t}
\]
or rearranging,
\[
Q = I \times t
\]
Step 2: Substitute the given values.
Given, \( I = 10 \, \text{A} \) and \( t = 2 \, \text{s} \):
\[
Q = 10 \times 2 = 20 \, \text{Coulomb}
\]
Step 3: Conclusion.
Therefore, the total charge passing through the conductor in 2 seconds is 20 coulomb.