Combination Of Resistors Series And Parallel

Step 1: Understanding the problem.
We are given a circuit with capacitors in series and parallel, and we are tasked with finding the equivalent capacitance. The given circuit configuration is:

- Two 2 capacitors in parallel.

- A 4 capacitor in series with the parallel combination.

- Two 1 capacitors in parallel.

- Another 4 capacitor in series with the combination of the 1 capacitors.

Step 2: Simplifying the parallel capacitors.
First, simplify the parallel capacitors: - For the two 2 capacitors in parallel, the total capacitance is: - For the two 1 capacitors in parallel, the total capacitance is:

Step 3: Simplifying the series capacitors.
Now, the equivalent capacitance of the two capacitors in series is calculated using the formula: For the parallel combination of 4 with 4 : Thus, .

Step 4: Total equivalent capacitance.
Now, combine the total capacitances: - The series combination of 2 with the parallel combination of 2 : So, .

Step 5: Conclusion.
The equivalent capacitance of the circuit is 1 , so the correct answer is 1 .

The total resistance of the parallel combination is:

,

so . Using Ohm’s law: