Three capacitors of `3 mu F,2 mu F` and `6 mu F` are connected in series. When a battery of `10 V` is connected to this combination then charge on `3 mu F` capacitor will be.

Options

A. `5 mu C`
B. `10 mu C`
C. `15 mu C`
D. `20 mu C`

Explanation

To solve the problem step by step, we need to find the charge on the 3 µF capacitor when three capacitors (3 µF, 2 µF, and 6 µF) are connected in series across a 10 V battery.

### Step 1: Calculate the equivalent capacitance of the series combination

For capacitors in series, the formula for equivalent capacitance \(C_{eq}\) is given by:

\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \]

Where \(C_1 = 3 \mu F\), \(C_2 = 2 \mu F\), and \(C_3 = 6 \mu F\).

Substituting the values:

\[ \frac{1}{C_{eq}} = \frac{1}{3} + \frac{1}{2} + \frac{1}{6} \]

### Step 2: Find a common denominator and simplify

The common denominator for 3, 2, and 6 is 6. Thus, we can rewrite each term:

\[ \frac{1}{C_{eq}} = \frac{2}{6} + \frac{3}{6} + \frac{1}{6} = \frac{2 + 3 + 1}{6} = \frac{6}{6} = 1 \]

So,

\[ C_{eq} = 1 \mu F \]

### Step 3: Calculate the total charge stored in the equivalent capacitor

The charge \(Q\) stored in a capacitor is given by the formula:

\[ Q = C_{eq} \times V \]

Where \(V = 10 V\). Thus,

\[ Q = 1 \mu F \times 10 V = 10 \mu C \]

### Step 4: Determine the charge on the 3 µF capacitor

In a series circuit, the charge on each capacitor is the same. Therefore, the charge on the 3 µF capacitor is also:

\[ Q_{3 \mu F} = 10 \mu C \]

### Final Answer

The charge on the 3 µF capacitor when a 10 V battery is connected is **10 µC**.

---