Question
Write the product of equivalent capacitances when 10 capacitors, each having a capacitance of $10 \mu F$, are connected in series and then parallel connection.
✓
Answer
Equivalent capacitance of series combination of $n$ capacitors will be
$ \frac{1}{C_{s}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\ldots \ldots+\frac{1}{C_n} $
There are 10 capacitors each with a capacitance of $10 \mu F$.All of these are combined into series combinations. Therefore the value of equivalence will be $1 \mu F$.
All these have been combined in parallel combination after series combination.
Formula of equivalency for parallel combination :
$C _{ P }= C _1+ C _2+ C _3 \ldots \ldots C _n$
$\begin{array}{r}\therefore C _{ P }=10+10+10+10+10+10+10+10+ \\ 10+10=100 \mu F\end{array}$
The product of both the capacitances
$= C _{ S } \times C _{ P }=1 \mu F \times 100 \mu F$
$=1 \times 10^{-6} F \times 100 \times 10^{-6} F$
$=10^{-10} F=1 A F$ Ans.
$ \frac{1}{C_{s}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\ldots \ldots+\frac{1}{C_n} $
There are 10 capacitors each with a capacitance of $10 \mu F$.All of these are combined into series combinations. Therefore the value of equivalence will be $1 \mu F$.
All these have been combined in parallel combination after series combination.
Formula of equivalency for parallel combination :
$C _{ P }= C _1+ C _2+ C _3 \ldots \ldots C _n$
$\begin{array}{r}\therefore C _{ P }=10+10+10+10+10+10+10+10+ \\ 10+10=100 \mu F\end{array}$
The product of both the capacitances
$= C _{ S } \times C _{ P }=1 \mu F \times 100 \mu F$
$=1 \times 10^{-6} F \times 100 \times 10^{-6} F$
$=10^{-10} F=1 A F$ Ans.
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