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1mF 2mF 3mF 2mF 2mF

1mF 2mF 3mF 2mF 2mF

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Determine the equivalent capacitance of the circuit shown

### Capacitors in Parallel and Series The diagram illustrates a complex combination of capacitors connected in both parallel and series configurations within an electrical circuit. Capacitors are devices that store electrical energy in an electric field and are characterized by their capacitance, measured in Farads (F). Here, capacitance is given in milliFarads (mF), where 1 mF = \(1 \times 10^{-3}\) F. #### Detailed Explanation of the Circuit - **Top Capacitor (Horizontally Aligned):** The circuit starts with a single 3mF capacitor at the top. - **Middle Row of Capacitors (Horizontally Aligned):** - The leftmost capacitor in this row has a capacitance of 1mF. - The middle capacitor in this row has a capacitance of 2mF. - The rightmost capacitor in this row has a capacitance of 3mF. - **Bottom Row of Capacitors (Horizontally Aligned):** - There are two parallel capacitors in the bottom row, each with a capacitance of 2mF. #### Series and Parallel Connections The configuration of these capacitors is as follows: 1. **Parallel Configuration:** - The three capacitors (1mF, 2mF, and 3mF) in the middle row are connected in parallel. - The two capacitors (both 2mF) in the bottom row are also connected in parallel. 2. **Series Configuration:** - The top 3mF capacitor and the parallel combination of the two 2mF capacitors are connected in series with the combined capacitances of the middle row capacitors. #### Calculating the Equivalent Capacitance 1. **Parallel Combination of Middle Row (1mF, 2mF, and 3mF):** - The total capacitance \(C_p\) is calculated by summing the individual capacitances: \[ C_p = 1\,mF + 2\,mF + 3\,mF = 6\,mF \] 2. **Parallel Combination of the Bottom Row (Two 2mF capacitors):** - The total capacitance \(C_{bottom}\) is calculated by summing the individual capacitances: \[ C_{bottom} = 2\,mF
Transcribed Image Text:### Capacitors in Parallel and Series The diagram illustrates a complex combination of capacitors connected in both parallel and series configurations within an electrical circuit. Capacitors are devices that store electrical energy in an electric field and are characterized by their capacitance, measured in Farads (F). Here, capacitance is given in milliFarads (mF), where 1 mF = \(1 \times 10^{-3}\) F. #### Detailed Explanation of the Circuit - **Top Capacitor (Horizontally Aligned):** The circuit starts with a single 3mF capacitor at the top. - **Middle Row of Capacitors (Horizontally Aligned):** - The leftmost capacitor in this row has a capacitance of 1mF. - The middle capacitor in this row has a capacitance of 2mF. - The rightmost capacitor in this row has a capacitance of 3mF. - **Bottom Row of Capacitors (Horizontally Aligned):** - There are two parallel capacitors in the bottom row, each with a capacitance of 2mF. #### Series and Parallel Connections The configuration of these capacitors is as follows: 1. **Parallel Configuration:** - The three capacitors (1mF, 2mF, and 3mF) in the middle row are connected in parallel. - The two capacitors (both 2mF) in the bottom row are also connected in parallel. 2. **Series Configuration:** - The top 3mF capacitor and the parallel combination of the two 2mF capacitors are connected in series with the combined capacitances of the middle row capacitors. #### Calculating the Equivalent Capacitance 1. **Parallel Combination of Middle Row (1mF, 2mF, and 3mF):** - The total capacitance \(C_p\) is calculated by summing the individual capacitances: \[ C_p = 1\,mF + 2\,mF + 3\,mF = 6\,mF \] 2. **Parallel Combination of the Bottom Row (Two 2mF capacitors):** - The total capacitance \(C_{bottom}\) is calculated by summing the individual capacitances: \[ C_{bottom} = 2\,mF
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