To solve for the voltage across the 8.8 μF capacitor, let's analyze the given capacitor network. The configuration of the capacitors is crucial in determining how they behave in the circuit.

The first step is identifying whether the capacitors are in series or parallel:

1. Identify Series and Parallel Capacitors:

   • The 4.95 μF and 12.5 μF capacitors are in parallel with each other.
   • This pair is then in series with the 8.8 μF capacitor.

2. Find the equivalent capacitance of the parallel combination: The formula for capacitors in parallel is: $C_{\text{eq, parallel}} = C_1 + C_2$ So for the 4.95 μF and 12.5 μF capacitors in parallel: $C_{\text{eq, parallel}} = 4.95 + 12.5 = 17.45 \, \mu\text{F}$

3. Calculate the total capacitance: Now, the total capacitance is determined by the series combination of the 17.45 μF and 8.8 μF capacitors. The formula for capacitors in series is: $\frac{1}{C_{\text{eq, series}}} = \frac{1}{C_1} + \frac{1}{C_2}$ $\frac{1}{C_{\text{eq, series}}} = \frac{1}{17.45} + \frac{1}{8.8}$ Calculate this to find the total capacitance.

4. Find the voltage across the 8.8 μF capacitor: Once the equivalent capacitance is found, use the voltage division rule to determine the voltage across the 8.8 μF capacitor. The voltage division formula is: $V_{\text{8.8}} = V_{\text{total}} \times \frac{C_{\text{eq, parallel}}}{C_{\text{eq, total}}}$

Now, let's go ahead and calculate each step to find the final voltage across the 8.8 μF capacitor. Given values C1 = 4.95 # μF C2 = 12.5 # μF C3 = 8.8 # μF V_total = 19.4 # V

Step 1: Calculate the equivalent capacitance for the parallel capacitors

C_parallel = C1 + C2

Step 2: Calculate the equivalent capacitance for the series combination

C_total_inv = 1/C_parallel + 1/C3 C_total = 1 / C_total_inv

Step 3: Calculate the voltage across the 8.8 μF capacitor (V_8.8)

V_8_8 = V_total * (C_parallel / C_total) V_8_8The voltage across the 8.8 μF capacitor is approximately 57.87 V.

Would you like further details or have any other questions?

Here are some related questions you might find interesting:

1. How does the equivalent capacitance change if the capacitors were arranged differently (e.g., all in series or all in parallel)?
2. What happens to the voltage distribution if the 19.4 V is replaced with a different voltage value?
3. How does the total energy stored in the system change when the total capacitance is increased?
4. What is the relationship between charge and voltage in capacitors, and how can this affect the overall energy in the system?
5. How would you calculate the charge on each capacitor in this network?

Tip: When working with capacitors, remember that series connections result in lower total capacitance, while parallel connections increase the total capacitance.