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

Options

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

Answer

To solve the problem of finding the charge on capacitors connected in series, we will follow these steps:

### Step 1: Identify the capacitance values
We have three capacitors with the following capacitance values:
- C1 = 3 µF
- C2 = 2 µF
- C3 = 6 µF

### Step 2: Calculate the equivalent capacitance
For capacitors in series, the formula for equivalent capacitance (C_eq) is given by:
\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \]
Substituting the values:
\[ \frac{1}{C_{eq}} = \frac{1}{3} + \frac{1}{2} + \frac{1}{6} \]

### Step 3: Find a common denominator
The least common multiple (LCM) of 3, 2, and 6 is 6. We can rewrite each term:
\[ \frac{1}{3} = \frac{2}{6}, \quad \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{6} = \frac{1}{6} \]
Now, substituting these values:
\[ \frac{1}{C_{eq}} = \frac{2}{6} + \frac{3}{6} + \frac{1}{6} = \frac{6}{6} = 1 \]

### Step 4: Calculate C_eq
Taking the reciprocal gives us:
\[ C_{eq} = 1 \, \mu F \]

### Step 5: Calculate the charge using the formula
The charge (Q) on the capacitors can be calculated using the formula:
\[ Q = C_{eq} \times V \]
Where V is the voltage across the capacitors. Given that V = 10 V:
\[ Q = 1 \, \mu F \times 10 \, V = 10 \, \mu C \]

### Final Answer
The charge on the capacitors when connected to a 10V battery is:
\[ \text{Charge (Q)} = 10 \, \mu C \]

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