Question

Three capacitors each of capacitance 9 μF, 3 μF ,18 μF are connected in series.The resultant capacitance of the combination *​

Answer 1

Given :

⟶ Three identical capacitors of capacitance 9uF, 3uF and 18uF are connected in series.

To Find :

➳ Equivalent capacitance of the series combination.

SoluTion :

⟹ Formula of equivalent capacitance of series combination is given by

$\bigstar\:\underline{\boxed{\bf{\dfrac{1}{C}=\dfrac{1}{C_1}+\dfrac{1}{C_2}+...+\dfrac{1}{C_n}}}}$

⟹ Charge on each capacitor remains same in series connection.

⟹ Formula of equivalent capacitance of parallel combination is given by

$\bigstar\:\underline{\boxed{\bf{C=C_1+C_2+...+C_n}}}$

⟹ Potential difference across each capacitor in parallel combination remains same.

$\dashrightarrow\tt\:\dfrac{1}{C}=\dfrac{1}{C_1}+\dfrac{1}{C_2}+\dfrac{1}{C_3}\\ \\ \dashrightarrow\tt\:\dfrac{1}{C}=\dfrac{1}{9}+\dfrac{1}{3}+\dfrac{1}{18}\\ \\ \dashrightarrow\tt\:\dfrac{1}{C}=\dfrac{4+12+2}{36}\\ \\ \dashrightarrow\tt\:C=\dfrac{36}{18}\\ \\ \dashrightarrow\underline{\boxed{\bf{C=2\:uF}}}\:\gray{\bigstar}$

Answer 2

$\sf{\underbrace{\red{To\:Find:-}}}$

• The resultant capacitance of the combination .

$\sf{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

• Three capacitors each of capacitance $\rm{9{\mu}F}$ , $\rm{3{\mu}F}$ and $\rm{18{\mu}F}$ are connected in series .

CONCEPT :-

☞ When “n” no. of capacitors are connected in series , then the Equivalent capacitance is,

$\bigstar\:\rm{\underline{\purple{\boxed{{\dfrac{1}{C}}\:=\:{\dfrac{1}{C_1}}\:+\:{\dfrac{1}{C_2}}\:+\:{\dfrac{1}{C_3}}\:+\:.....\:{\dfrac{1}{C_n}}\:}}}}$

__________________________

• Charge on each capacitor connected in series is remain same

• But Potential difference across each capacitor connected in series is different .

CALCULATION :-

$\rm\underline{\green{\boxed{\implies{\dfrac{1}{C}}\:=\:{\dfrac{1}{C_1}}\:+\:{\dfrac{1}{C_2}}\:+\:{\dfrac{1}{C_3}}\:}}}$

$\rm{\implies\:{\dfrac{1}{C}}\:=\:{\dfrac{1}{9}}\:+\:{\dfrac{1}{3}}\:+\:{\dfrac{1}{18}}\:}$

$\rm{\implies\:{\dfrac{1}{C}}\:=\:{\dfrac{18}{36}}\:}$

$\rm{\implies\:C\:=\:{\dfrac{36}{18}}\:}$

$\checkmark\:\rm{\underline{\blue{\boxed{\implies\:C\:=\:2{\mu}F\:}}}}$