Complete the following statements with an appropriate word /term be filled in the blank space(s).

The equivalent capacitance C for the series combination of three capacitance $C_{1}, C_{2}$ and $C_{3}$ is given by $\frac{1}{C} =$ ..............

C_{1} + C_{2} + C_{3}

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(\frac{1}{C_{1} + C_{2} + C_{3}})

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⎛ ⎜ ⎜ ⎜ ⎝ \frac{1}{\frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}}} ⎞ ⎟ ⎟ ⎟ ⎠

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(\frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}})

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Solution

The correct option is D $(\frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}})$
When in series, the reciprocal of the net capacitance is equal to the sum of reciprocal of individual capacitances.
The equivalent capacitance of the pair of capacitors is $C = \frac{Q}{V}$
$\frac{1}{C} = \frac{V}{Q} = \frac{(v_{1} + v_{2} + v_{3})}{Q} = \frac{v_{1}}{Q} + \frac{v_{2}}{Q} + \frac{v_{3}}{Q} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}}$

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