There are 7 identical capacitors. The equivalent capacitance when they are connected in series is C. The equivalent capacitance when they are connected in parallel is

Options

A. C/49
B. C/7
C. 7C
D. 49 C

Answer

To solve the problem step by step, we will first determine the capacitance of each capacitor and then find the equivalent capacitance when they are connected in parallel.

### Step 1: Determine the capacitance of each capacitor

Let the capacitance of each identical capacitor be \( C_0 \). When the 7 capacitors are connected in series, the formula for equivalent capacitance \( C \) is given by:

\[ \frac{1}{C} = \frac{1}{C_0} + \frac{1}{C_0} + \frac{1}{C_0} + \frac{1}{C_0} + \frac{1}{C_0} + \frac{1}{C_0} + \frac{1}{C_0} \]

This simplifies to:

\[ \frac{1}{C} = \frac{7}{C_0} \]

### Step 2: Solve for \( C_0 \)

From the equation above, we can rearrange it to find \( C_0 \):

\[ C_0 = 7C \]

### Step 3: Calculate the equivalent capacitance when connected in parallel

When the same 7 capacitors are connected in parallel, the equivalent capacitance \( C_{eq} \) is simply the sum of the individual capacitances:

\[ C_{eq} = C_0 + C_0 + C_0 + C_0 + C_0 + C_0 + C_0 \]

This simplifies to:

\[ C_{eq} = 7C_0 \]

### Step 4: Substitute the value of \( C_0 \)

Now, substitute the value of \( C_0 \) that we found earlier:

\[ C_{eq} = 7(7C) = 49C \]

### Final Answer

Thus, the equivalent capacitance when the 7 identical capacitors are connected in parallel is:

\[ C_{eq} = 49C \]

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