Step 1: Apply Ohm's Law.
Ohm’s Law states that the current \( I \) through a resistor is given by:
\[
I = \frac{V}{R}
\]
where:
- \( V \) is the potential difference across the resistor,
- \( R \) is the resistance.
Step 2: Calculate the total voltage across the resistor.
The total voltage across the resistor is the difference between the two voltage sources:
\[
V = 6V - 5V = 1V
\]
Step 3: Calculate the current.
Now, using the value of \( R = 100Ω \) and \( V = 1V \), we can calculate the current:
\[
I = \frac{1V}{100Ω} = 10 \, \text{mA}
\]
Step 4: Conclusion.
The current flowing in the circuit is \( 10 \, \text{mA} \), so the correct answer is (A).