To determine the amount of charge that flows from a \(3\) V battery when it is connected to a \(9.00 \) microfarad (\(\mu\)F) capacitor, we use the relationship between charge (\(Q\)), capacitance (\(C\)), and voltage (\(V\)), given by the formula:
[tex]\[ Q = C \times V \][/tex]
Here are the steps to solve the problem:
1. Identify the given values:
- Voltage (\(V\)) = \(3\) V
- Capacitance (\(C\)) = \(9.00\) \(\mu\)F
2. Convert the capacitance from microfarads to farads:
- \(1 \, \mu\text{F} = 10^{-6} \text{F}\)
- Therefore, \(9.00 \, \mu\text{F}\) = \(9.00 \times 10^{-6} \text{F}\)
3. Substitute the values into the formula:
[tex]\[ Q = (9.00 \times 10^{-6} \text{F}) \times (3 \text{ V}) \][/tex]
4. Calculate the charge (Q):
[tex]\[ Q = 2.7 \times 10^{-5} \text{C} \][/tex]
Therefore, the amount of charge that flows from the \(3\) V battery when connected to a \(9.00 \mu\text{F}\) capacitor is \(2.7 \times 10^{-5} \text{C}\).
Among the given options, the correct answer is:
[tex]\[ \boxed{2.7 \times 10^{-5} \text{C}} \][/tex]
