The value of Ceq in the given circuit is:

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  1. 4 μF
  2. 11.76 μF
  3. 11.76 mF
  4. 4 mF

Answer (Detailed Solution Below)

Option 4 : 4 mF
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Concept:

Capacitors in series and parallel combine differently:

  • Series: \( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots \)
  • Parallel: \( C_{eq} = C_1 + C_2 + \dots \)

Step 1: Combine 12 mF and 4 mF in series

\[ \frac{1}{C_1} = \frac{1}{12} + \frac{1}{4} = \frac{1 + 3}{12} = \frac{4}{12} \Rightarrow C_1 = \frac{12}{4} = 3 \, \text{mF} \]

Step 2: Combine result with 9 mF in parallel

\[ C_2 = 3 + 9 = 12 \, \text{mF} \]

Step 3: Combine C2 with 6 mF in series

\[ \frac{1}{C_{eq}} = \frac{1}{6} + \frac{1}{12} = \frac{2 + 1}{12} = \frac{3}{12} \Rightarrow C_{eq} = \frac{12}{3} = 4 \, \text{mF} \]

 

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