Question

Three capacitors each of capacity C are connected in series. The resultant capacity will be

Answer 1

Given :

Three capacitance each of capacity C are connected in series.

To Find :

Equivalent resistance of the connection.

Solution :

❒ Let's derive formula of equivalent capacitance for series connection.

Let three capacitors (C₁, C₂ and C₃) are connected in series across a battery of voltage V.

• p.d. across C₁ = V₁
• p.d. across C₂ = V₂
• p.d. across C₃ = V₃

We know that equal amount of charge distributes on each capacitor in series connection.

Let charge on each capacitor be Q.

Capacitance of a parallel plate capacitor is given by, C = Q/V

$:\implies\sf\:V=V_1+V_2+V_3$

$:\implies\sf\:\dfrac{Q}{C_{eq}}=\dfrac{Q}{C_1}+\dfrac{Q}{C_2}+\dfrac{Q}{C_3}$

$:\implies\bf\:\dfrac{1}{C_{eq}}=\dfrac{1}{C_1}+\dfrac{1}{C_2}+\dfrac{1}{C_3}$

• ATQ, C₁ = C₂ = C₃ = C

$:\implies\sf\:\dfrac{1}{C_{eq}}=\dfrac{1}{C}+\dfrac{1}{C}+\dfrac{1}{C}$

$:\implies\sf\:\dfrac{1}{C_{eq}}=\dfrac{3}{C}$

$:\implies\:\underline{\boxed{\bf{\purple{C_{eq}=\dfrac{C}{3}}}}}$

Answer 2

${ \huge{ \underline{ \underline{ \underline{ \underline{ \underline{ \sf{ \orange{Required \: Answer : }}}}}}}}}$

$\\ \sf{ \frac{1}{c} \: series = \frac{1}{c1} + \frac{1}{c2} + \frac{1}{c3} } \\ \\ \sf{c1 \: = \: c2 \: = \: c3 = \: c} \\ \\ \sf{ \frac{1}{c} + \frac{1}{c} + \frac{1}{c}} \\ \\ \sf{ = \frac{c}{3} }$