Seven capacitors each of capacitance 2$\mu$F are to be connected in a configuration to obtain an effective capacitance (10/11)$\mu$F. The combination is \dots
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When designing circuits, if the target equivalent capacitance ($10/11 \approx 0.9$) is significantly smaller than the individual capacitance ($2.0$), the dominant macro-structure of the circuit must be a series configuration.
Step 1: Understanding the Question:
We have exactly 7 identical capacitors ($C = 2\mu$F). We must deduce the correct electrical circuit wiring configuration (from visually provided options) that yields a highly specific total equivalent capacitance of $C_{eq} = 10/11 \, \mu$F. Step 2: Key Formula or Approach:
1. Capacitors in Parallel add linearly: $C_p = C_1 + C_2 + \dots$
2. Capacitors in Series add reciprocally: $\frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$
We need to manipulate the desired equivalent fraction $\frac{10}{11}$ to see how it can be built from fractions of $\frac{1}{2}$. Step 3: Detailed Explanation:
The target equivalent capacitance is $C_{eq} = \frac{10}{11} \, \mu$F.
Let's look at the reciprocal, which represents a primary series connection format:
$$\frac{1}{C_{eq}} = \frac{11}{10}$$
We need to break the fraction $\frac{11}{10}$ into a sum of reciprocal capacitances using our given $C = 2\mu$F (so individual series blocks contribute $\frac{1}{2}$).
Notice that $\frac{11}{10} = 1 + \frac{1}{10}$.
Let's break the integer $1$ down using halves: $1 = \frac{1}{2} + \frac{1}{2}$.
So, the total reciprocal equation is:
$$\frac{1}{C_{eq}} = \frac{1}{2} + \frac{1}{2} + \frac{1}{10}$$
Let's interpret these three distinct terms:
- The first term $\frac{1}{2}$ represents one single $2\mu$F capacitor in series.
- The second term $\frac{1}{2}$ represents another single $2\mu$F capacitor in series.
- The third term $\frac{1}{10}$ represents a single block of capacitance equal to $10\mu$F.
How do we get $10\mu$F using only $2\mu$F capacitors? We put exactly 5 of them in parallel! ($5 \times 2\mu\text{F} = 10\mu\text{F}$).
Therefore, the complete circuit requires:
1 single cap + 1 single cap + a parallel block of 5 caps = 7 total capacitors.
This perfectly matches the required number of components. The visual diagram for this is a block of 5 parallel branches placed in series with 2 sequential capacitors. Step 4: Final Answer:
The correct combination is option (c), depicting 5 capacitors in parallel connected in series with the remaining 2.
