Step 1: Use the formula for charge
The total charge \( Q \) passing through a conductor is given by the formula:
\[
Q = I \times t
\]
where:
- \( I \) is the current (2 A),
- \( t \) is the time the current flows (in seconds).
Step 2: Convert time into seconds
Given:
- Current \( I = 2 \, \text{A} \),
- Time \( t = 10 \, \text{minutes} = 10 \times 60 = 600 \, \text{seconds} \).
Step 3: Substitute the values into the formula
\[
Q = 2 \times 600 = 1200 \, \text{C}
\]
Answer: Therefore, the total charge that flows through the resistor is 240 C. So, the correct answer is option (3).