Question

In the figure below, the capacitance of each capacitor is $ 3 \mu F $. The effective capacitance between A and B is

• A. \( \frac{1}{4} \mu F \)
• B. \( 3 \mu F \)
• C. \( 6 \mu F \)
• D. \( 5 \mu F \)

Hint:

When capacitors are connected in parallel, their total capacitance is the sum of the individual capacitances.

Answer 1

The Correct Option is D

To determine the equivalent capacitance of the given capacitor network, we analyze the circuit step-by-step.

1. Given Capacitances:
All capacitors have equal values:
$ C_1 = C_2 = C_3 = C_4 = 3 \, \mu \text{F} $

2. Parallel Combination (C₃ and C₄):
For parallel capacitors:
$ C_{\text{parallel}} = C_3 + C_4 = 3 + 3 = 6 \, \mu \text{F} $

3. Series Combination (C₂ and C_parallel):
For series capacitors:
$ \frac{1}{C_{\text{series}}} = \frac{1}{C_2} + \frac{1}{C_{\text{parallel}}} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2} $
Thus:
$ C_{\text{series}} = 2 \, \mu \text{F} $

4. Final Parallel Combination (C₁ and C_series):
The equivalent capacitance becomes:
$ C_{\text{final}} = C_1 + C_{\text{series}} = 3 + 2 = 5 \, \mu \text{F} $

Final Answer:
The equivalent capacitance of the network is $5 \, \mu \text{F}$.

Answer 2

To determine the effective capacitance between points A and B, we must analyze how the capacitors are arranged in the circuit. Let's assume the arrangement is a combination of series and parallel configurations, a common scenario in such problems.

Step 1: Identify Configuration
The given capacitors all have a capacitance of \( 3 \mu F \). Analyzing the series and parallel groupings of these capacitors will guide us in calculating the total capacitance effectively.

Step 2: Series Combination
In a series configuration, the reciprocal of the total capacitance (\( C_s \)) is given by:
\[ \frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} + \dots + \frac{1}{C_n} \]
Assuming one or more series connections, apply this formula to the respective group.

Step 3: Parallel Combination
In a parallel configuration, the total capacitance (\( C_p \)) is given by the sum of individual capacitances:
\[ C_p = C_1 + C_2 + \dots + C_n \]
Identify the parallel sections in the arrangement and apply this formula.

Step 4: Combine Results
After computing the capacitances for series and parallel sections, combine them based on their specific arrangement in the circuit.

Final Calculation:
For the given setup, appropriate combination of series-parallel calculations will result in a total effective capacitance of:
\[ C_{\text{effective}} = 5 \mu F \]
Therefore, the effective capacitance between points A and B is \( 5 \mu F \).