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A combination of series and parallel connections of capacitors is shown in the figure. Express the total capacitance of this combination in terms of the capacitances C1 through C6.
![This diagram represents a complex circuit consisting of six capacitors labeled \( C_1, C_2, C_3, C_4, C_5, \) and \( C_6 \).
**Description:**
1. **Series and Parallel Configuration**:
- \( C_1 \), \( C_2 \), and \( C_3 \) are connected in series. In series circuits, the equivalent capacitance is determined by the reciprocal formula:
\[
\frac{1}{C_{\text{eq1}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}
\]
2. **Parallel Connection**:
- \( C_4 \) is connected in parallel with the series combination of \( C_1, C_2, \) and \( C_3 \). The total capacitance for capacitors in parallel is simply the sum:
\[
C_{\text{eq2}} = C_4 + C_{\text{eq1}}
\]
3. **Additional Series Connection**:
- Following \( C_4 \), \( C_5 \) and \( C_6 \) are connected in parallel. The total capacitance of \( C_5 \) and \( C_6 \) is:
\[
C_{\text{eq3}} = C_5 + C_6
\]
4. **Final Circuit Combination**:
- The total capacitance of the circuit is a combination of the parallel section (\( C_{\text{eq2}} \)) and the parallel capacitors \( C_5 \) and \( C_6 \).
**Educational Implication**:
This diagram serves as an example of how capacitors can be arranged in both series and parallel configurations in a circuit. Understanding such combinations is crucial for analyzing complex circuits in electronics and can help in determining the overall capacitance of a system.](https://content.bartleby.com/qna-images/question/50773906-f3e8-400c-986e-219d096789cc/f292bdde-b14f-48b8-a15a-18fb81a8b46f/guxnhzi_processed.jpeg)
Transcribed Image Text:This diagram represents a complex circuit consisting of six capacitors labeled \( C_1, C_2, C_3, C_4, C_5, \) and \( C_6 \).
**Description:**
1. **Series and Parallel Configuration**:
- \( C_1 \), \( C_2 \), and \( C_3 \) are connected in series. In series circuits, the equivalent capacitance is determined by the reciprocal formula:
\[
\frac{1}{C_{\text{eq1}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}
\]
2. **Parallel Connection**:
- \( C_4 \) is connected in parallel with the series combination of \( C_1, C_2, \) and \( C_3 \). The total capacitance for capacitors in parallel is simply the sum:
\[
C_{\text{eq2}} = C_4 + C_{\text{eq1}}
\]
3. **Additional Series Connection**:
- Following \( C_4 \), \( C_5 \) and \( C_6 \) are connected in parallel. The total capacitance of \( C_5 \) and \( C_6 \) is:
\[
C_{\text{eq3}} = C_5 + C_6
\]
4. **Final Circuit Combination**:
- The total capacitance of the circuit is a combination of the parallel section (\( C_{\text{eq2}} \)) and the parallel capacitors \( C_5 \) and \( C_6 \).
**Educational Implication**:
This diagram serves as an example of how capacitors can be arranged in both series and parallel configurations in a circuit. Understanding such combinations is crucial for analyzing complex circuits in electronics and can help in determining the overall capacitance of a system.
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