Question

Three capacitors of capacitances 3$\mu F$ are available. The minimum and maximum capacitances, which may be obtained, are:

Answer 1

In order to answer this question, we need to understand the concepts of combination of capacitances in different arrangements. These arrangements are namely known as series and parallel arrangements. These arrangements are utilized in different scenarios according to the need of the capacitances.
Complete step by step answer:
In a number of applications, many capacitors can be connected together. Multiple capacitor connections function as a single equivalent capacitor. The capacitance of the final capacitor is determined by the individual capacitors as well as how they are connected. The terms "series" and "parallel" refer to two different types of linkages.
The capacitance in total is less than the individual capacitances of the series capacitors when they are connected in a series combination. When one, two, or more capacitors are linked in series, the result is a single or equivalent capacitor with the sum of the spacings between the plates of the individual capacitors. With all other elements remaining constant, an increase in plate spacing leads in a decrease in capacitance.
Series formula: $\dfrac{1}{C} = \dfrac{1}{{{C_1}}} + \dfrac{1}{{{C_2}}} + ........... + \dfrac{1}{{{C_n}}}$
The total capacitance of a series of parallel capacitors is simply the sum of their individual capacitance values. The number of capacitors that can be linked in parallel is theoretically unlimited. But, depending on the application, area, and other physical constraints, there will undoubtedly be practical limitations.
Parallel formula: $C = {C_1} + {C_2} + ........... + {C_n}$
The minimum capacitance can be observed in series arrangement.
$\dfrac{1}{{{C_{\min }}}} = \dfrac{1}{3} + \dfrac{1}{3} + \dfrac{1}{3} \\\ {C_{\min }} = 1\mu F \\\$
The maximum capacitance can be observed in parallel arrangement.
${C_{\max }} = 3 + 3 + 3 \\\ {C_{\max }} = 9\mu F \\\$

Note: A capacitor is a two-terminal electrical component that may store energy in the form of an electric charge. It is made up of two electrical wires separated by a certain distance. The space between the conductors can be filled with vacuum or a dielectric, which is an insulating substance.