Capacitors And Capacitance

To determine the equivalent capacitance of the given capacitor network, we analyze the circuit step-by-step.

1. Given Capacitances:
All capacitors have equal values:

2. Parallel Combination (C₃ and C₄):
For parallel capacitors:

3. Series Combination (C₂ and C_parallel):
For series capacitors:

Thus:

4. Final Parallel Combination (C₁ and C_series):
The equivalent capacitance becomes:

Final Answer:
The equivalent capacitance of the network is .

We are given: - Dielectric constant , - Dielectric strength ,
- Voltage rating ,
- Capacitance .
The maximum electric field the capacitor can handle is 10% of its dielectric strength, so the maximum electric field is: Now, using the relationship between the voltage, electric field, and separation between the plates for a parallel plate capacitor: where is the separation between the plates. Rearranging for : The capacitance of a parallel plate capacitor is given by: where: - is the permittivity of free space, - is the dielectric constant, - is the area of the plates, and - is the separation between the plates. Substituting the given values into the formula: Simplifying:
Thus, the minimum area of the plates required is .

The network consists of capacitors connected in series and parallel. To calculate the charge on the capacitors, we first need to find the equivalent capacitance.

Step 1: Combine Capacitors in Series and Parallel
The capacitor and one capacitor are in parallel:

Step 2: Combine with the Next Capacitor in Series
Now, the equivalent capacitor is in series with the next capacitor:

Step 3: Combine with the Last Capacitor in Parallel
The final capacitor is in parallel with the equivalent capacitance :

Step 4: Use the Formula for Charge
The total charge supplied by the battery is: The charge on each of the capacitors is:
Thus, the charge acquired by each capacitor is .