Determine the voltage drops and the energy stored in the steady state across each of the four capacitors in the circuit shown below. 12 uF 5 uF 10 V 4 µF HE 6 µF

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**Educational Resource: Analyzing Capacitor Voltage Drops and Energy Storage**

Determine the voltage drops and the energy stored in the steady state across each of the four capacitors in the circuit shown below.

**Circuit Diagram Description:**

The circuit consists of a series-parallel arrangement of capacitors connected to a 10V power supply. Here is a detailed explanation of the configuration:

1. **Components:**
   - **Power Supply:** 10V 
   - **Capacitors:**
     - 5 μF (microfarads)
     - 6 μF 
     - 12 μF
     - 4 μF

2. **Configuration:**
   - The 5 μF and 6 μF capacitors are in parallel.
   - This parallel combination is in series with a 10V power supply.
   - Across this series are also the 12 μF and 4 μF capacitors, and they are in parallel with each other.

**Objective:**

Calculate:
- Voltage drops across each capacitor.
- Energy stored in each capacitor.

**Analytical Approach:**

1. **Identify Series and Parallel Relationships:**
   - The capacitors in parallel (5 μF with 6 μF, and 12 μF with 4 μF) should be combined to find equivalent capacitance.

2. **Use Capacitance Formulas:**
   - For capacitors in parallel: \(C_{\text{total}} = C_1 + C_2 + \cdots + C_n\)
   - For capacitors in series: \( \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}\)

3. **Voltage and Energy Calculations:**
   - Voltage drop across parallel capacitors is the same as the power supply.
   - Energy stored in a capacitor: \(E = \frac{1}{2}CV^2\), where \(C\) is capacitance and \(V\) is voltage across the capacitor.

By applying these principles to the given circuit, each capacitor's voltage drop and stored energy can be determined accurately.
Transcribed Image Text:**Educational Resource: Analyzing Capacitor Voltage Drops and Energy Storage** Determine the voltage drops and the energy stored in the steady state across each of the four capacitors in the circuit shown below. **Circuit Diagram Description:** The circuit consists of a series-parallel arrangement of capacitors connected to a 10V power supply. Here is a detailed explanation of the configuration: 1. **Components:** - **Power Supply:** 10V - **Capacitors:** - 5 μF (microfarads) - 6 μF - 12 μF - 4 μF 2. **Configuration:** - The 5 μF and 6 μF capacitors are in parallel. - This parallel combination is in series with a 10V power supply. - Across this series are also the 12 μF and 4 μF capacitors, and they are in parallel with each other. **Objective:** Calculate: - Voltage drops across each capacitor. - Energy stored in each capacitor. **Analytical Approach:** 1. **Identify Series and Parallel Relationships:** - The capacitors in parallel (5 μF with 6 μF, and 12 μF with 4 μF) should be combined to find equivalent capacitance. 2. **Use Capacitance Formulas:** - For capacitors in parallel: \(C_{\text{total}} = C_1 + C_2 + \cdots + C_n\) - For capacitors in series: \( \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}\) 3. **Voltage and Energy Calculations:** - Voltage drop across parallel capacitors is the same as the power supply. - Energy stored in a capacitor: \(E = \frac{1}{2}CV^2\), where \(C\) is capacitance and \(V\) is voltage across the capacitor. By applying these principles to the given circuit, each capacitor's voltage drop and stored energy can be determined accurately.
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