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Seven capacitors each of capacitance $2\mu F$ are to be connected in a configuration to obtain an effective capacitance of $\dfrac{{10}}{{11}}\mu F$. Which of the following combinations shown below will achieve the desired result?




Last updated date: 17th Apr 2024
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Hint:In several capacitors can be connected together to be used in a variety of applications. Multiple connections of capacitors behave as one equivalent capacitor. Capacitors are often arranged in two, simple and customary sorts of connections, referred to as series and parallel. The sum of total capacitance calculation is, ${C_P} = {C_{1 + }}{C_2} + {C_3} + ...........$

Complete step by step answer:
When the equivalent capacitance for the given parallel combination, it can be found by using formula for,
${C_{eq}} = {C_1} + {C_2} + {C_3} + .........$
And, the equivalent capacitance for series combination are often found by using formula
$\dfrac{1}{{{C_{eq}}}} = \dfrac{1}{{{C_1}}} + \dfrac{1}{{{C_2}}} + \dfrac{1}{{{C_3}}} + .........$

When option A is,
Two capacitor are in serial with the mixture combination of \[5\] capacitor in parallel
So, $\dfrac{1}{{{C_{eq}}}} = \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{{(2 + 2 + 2 + 2 + 2)}}$
On simplification we get,
$ \Rightarrow {C_{eq}} = \dfrac{{10}}{{11}}\mu F$

Therefore, option (A) is the correct answer.

Additional Information:
The one and only standard components in electronic circuits are called capacitors.
Also, we can observe that the complicated combination of any capacitors occurs in the practical circuits. So we can say that it is useful to possess a group of rules for some general arrangements of capacitors and it is locating the equivalent capacitance. It seems that we will always find the equivalent capacitance by repeated application of two simple rules. These rules are associated with capacitors connected serial and in parallel.

Note: Capacitors serial and Parallel a capacitor is especially used for storing electric energy like electrostatic energy. Once there's a requirement to reinforce more energy to store capacity, then an appropriate capacitor with increased capacitance is often necessary.