Determine all the values of equivalent capacitance you can create using any combination of three identical capacitors with capacitance \(C\).

When all three capacitors are connected in series, the equivalent capacitance C_eq1 can be found using the formula: \(\frac{1}{C_{eq1}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C}\) Which simplifies to: \(\frac{1}{C_{eq1}} = \frac{3}{C}\) And then: \(C_{eq1} = \frac{C}{3}\)

When two capacitors are connected in parallel and the third one is connected in series with this pair, the equivalent capacitance C_eq2 can be found using the following steps: 1. Find the equivalent capacitance of the two capacitors in parallel (C_12). The formula for the equivalent capacitance of capacitors in parallel is: \(C_{12} = C + C = 2C\) 2. Now, find the equivalent capacitance of C_12 and the third capacitor C connected in series. Using the formula for the equivalent capacitance of capacitors in series: \(\frac{1}{C_{eq2}} = \frac{1}{C_{12}} + \frac{1}{C}\) Substitute the value of C_12: \(\frac{1}{C_{eq2}} = \frac{1}{2C} + \frac{1}{C}\) Simplifying, we get: \(\frac{1}{C_{eq2}} = \frac{3}{2C}\) And then: \(C_{eq2} = \frac{2C}{3}\)

When all three capacitors are connected in parallel, the equivalent capacitance C_eq3 can be found using the formula: \(C_{eq3} = C + C + C = 3C\)

There are three possible equivalents capacitances that can be created using any combination of three identical capacitors with capacitance C: 1. All capacitors in series: \(C_{eq1} = \frac{C}{3}\) 2. Two capacitors in parallel, and the third one in series: \(C_{eq2} = \frac{2C}{3}\) 3. All capacitors in parallel: \(C_{eq3} = 3C\) These are all the possible values of equivalent capacitance that can be created using three identical capacitors with capacitance C.