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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? A) B) C)  D)

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, ${C_P} = {C_{1 + }}{C_2} + {C_3} + ...........$

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.