Two capacitors with `C_A` greater than `C_B` and are connected in series with a battery. Which of the following is true?

Options

A. There is move charge stored on `C_A`
B. There is more charge stored on `C_B`
C. There is the same charge stored on each capacitor
D. There is the same potential difference across both capacitors

Answer

To solve the question regarding two capacitors \(C_A\) and \(C_B\) connected in series with a battery, we can follow these steps:

### Step 1: Understand the Series Connection of Capacitors
In a series connection, the same charge \(Q\) flows through each capacitor. This means that the charge on both capacitors is equal.

**Hint:** Remember that in a series circuit, the charge on each component is the same.

### Step 2: Analyze the Charge on Each Capacitor
Since the capacitors are in series, the charge on capacitor \(C_A\) is equal to the charge on capacitor \(C_B\):
\[ Q_A = Q_B = Q \]

**Hint:** Use the concept of charge conservation in series circuits.

### Step 3: Relate Charge and Capacitance to Potential Difference
The potential difference across each capacitor can be expressed using the formula:
\[ V = \frac{Q}{C} \]
For capacitor \(C_A\):
\[ V_A = \frac{Q}{C_A} \]
For capacitor \(C_B\):
\[ V_B = \frac{Q}{C_B} \]

**Hint:** Remember that the potential difference across a capacitor is inversely proportional to its capacitance.

### Step 4: Compare the Potential Differences
Since \(C_A > C_B\), we can conclude:
\[ V_A < V_B \]
This means that the potential difference across capacitor \(C_A\) is less than that across capacitor \(C_B\).

**Hint:** Think about how capacitance affects the voltage drop across each capacitor.

### Step 5: Conclusion
From the analysis, we can conclude that:
- The charge on both capacitors is the same.
- The potential difference across each capacitor is different, with \(V_A < V_B\).

Thus, the correct statement is that there is the same charge stored on each capacitor.

**Final Answer:** The correct option is that there is the same charge stored on each capacitor.