Four Capacitors of capacitance `2muF` each are connected in series. What will be the capacitance of the equivalent capacitors ?

Options

A. `0.2 mu F`
B. `0.4 mu F`
C. `0.5 mu F`
D. `0.8 muF`

Answer

To find the equivalent capacitance of four capacitors connected in series, we can follow these steps:

### Step 1: Understand the Series Connection
In a series connection, the total or equivalent capacitance (C_eq) can be found using the formula:
\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \frac{1}{C_4} \]
where \(C_1, C_2, C_3, C_4\) are the capacitances of the individual capacitors.

### Step 2: Identify the Values
Given that each capacitor has a capacitance of \(2 \mu F\):
- \(C_1 = 2 \mu F\)
- \(C_2 = 2 \mu F\)
- \(C_3 = 2 \mu F\)
- \(C_4 = 2 \mu F\)

### Step 3: Substitute the Values into the Formula
Substituting the values into the formula:
\[ \frac{1}{C_{eq}} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} \]

### Step 4: Calculate the Right Side
Calculating the right side:
\[ \frac{1}{C_{eq}} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{4}{2} = 2 \]

### Step 5: Find the Equivalent Capacitance
Now, take the reciprocal to find \(C_{eq}\):
\[ C_{eq} = \frac{1}{2} \mu F = 0.5 \mu F \]

### Final Answer
The equivalent capacitance of the four capacitors connected in series is:
\[ C_{eq} = 0.5 \mu F \]

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