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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.
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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