To determine the electrical energy stored in the capacitors of the given circuit, we need to first understand the configuration and then calculate the total capacitance, voltage across each capacitor, and finally the energy stored.

1. Identify the Configuration:

   • Capacitors $C_1$ and $C_2$ are in series.
   • Capacitors $C_3$ and $C_4$ are also in series.
   • These two series combinations are in parallel with $C_5$.

2. Calculate Equivalent Capacitance:

   • For series capacitors $C_1$ (4F) and $C_2$ (3F): $\frac{1}{C_{12}} = \frac{1}{C_1} + \frac{1}{C_2} = \frac{1}{4} + \frac{1}{3} = \frac{7}{12} \implies C_{12} = \frac{12}{7} \text{ F}$

   • For series capacitors $C_3$ (2F) and $C_4$ (1F): $\frac{1}{C_{34}} = \frac{1}{C_3} + \frac{1}{C_4} = \frac{1}{2} + \frac{1}{1} = \frac{3}{2} \implies C_{34} = \frac{2}{3} \text{ F}$

   • The combined capacitance $C_{12}$ and $C_{34}$ are in parallel with $C_5$ (6F): $C_{\text{eq}} = C_{12} + C_{34} + C_5 = \frac{12}{7} + \frac{2}{3} + 6$ Converting to a common denominator: $\frac{12}{7} = \frac{36}{21}, \quad \frac{2}{3} = \frac{14}{21}, \quad 6 = \frac{126}{21}$ $C_{\text{eq}} = \frac{36}{21} + \frac{14}{21} + \frac{126}{21} = \frac{176}{21} \approx 8.38 \text{ F}$

3. Calculate Energy Stored: The energy stored in a capacitor is given by: $E = \frac{1}{2} C V^2$ Here, $V = 6 \text{ volts}$ and $C_{\text{eq}} \approx 8.38 \text{ F}$: $E = \frac{1}{2} \times 8.38 \times 6^2 = \frac{1}{2} \times 8.38 \times 36 = 150.84 \text{ joules}$

Therefore, the electrical energy stored in the capacitors is approximately 150.84 joules.

Do you want any further details or have any other questions?

Here are some related questions you might be interested in:

1. How do you calculate the voltage across each capacitor in a series-parallel circuit?
2. What happens to the energy stored when capacitors are connected in series versus parallel?
3. How can you determine the charge on each capacitor in the circuit?
4. What is the impact of different voltage sources on the energy stored in capacitors?
5. How does changing the capacitance of one capacitor affect the total capacitance in a series-parallel circuit?

Tip: Always remember to convert all your capacitors to a common equivalent capacitance to simplify calculations in series-parallel circuits.