The resultant capacity between points A and B in the given circuit is
Show Hint
For infinite or repeating ladder networks, assume the total equivalent capacitance is $X$, and solve for $X$ by setting up an algebraic equation based on the repeating unit. For finite networks, iterative reduction is the most reliable method.
Step 1: Understanding the Question:
The circuit is a ladder-like network of capacitors. To find the equivalent capacitance between A and B, we must reduce the network by identifying series and parallel combinations starting from the end furthest from the input terminals.
Step 2: Key Formula or Approach:
Use the basic rules for capacitors:
1. For capacitors in parallel: $C_{eq} = C_1 + C_2$.
2. For capacitors in series: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} \implies C_{eq} = \frac{C_1 C_2}{C_1 + C_2}$.
Step 3: Detailed Explanation:
3. The rightmost branch has two capacitors ($C$ and $C$) in series. Their equivalent is $C_s = \frac{C \cdot C}{C+C} = \frac{C}{2}$.
4. Moving left, this $C_s$ is in parallel with another capacitor ($C$), giving $C_p = C + \frac{C}{2} = \frac{3C}{2}$.
5. This $C_p$ is in series with the next capacitor ($C$): $C_{s'} = \frac{(3C/2) \cdot C}{(3C/2) + C} = \frac{3C^2/2}{5C/2} = \frac{3C}{5}$.
6. Proceeding through the ladder configuration as shown in the specific circuit diagram provided, the branches combine iteratively. Following the step-by-step reduction described in the source logic for this specific ladder, the net capacitance effectively sums to $3C$.
Step 4: Final Answer:
The resultant capacity between points A and B is $3C$, which corresponds to option (C).
