Question

A network of six identical capacitors, each of value C, is made as shown in the figure. The equivalent
capacitance between the points A and B is :-
​

Answer 1

SoLuTioN :

⏭ Given :

✏ A network of six identical capacitors, each of value C, is made as shown in the figure.

⏭ To Find :

✏ The equivalent capacitance between the points A and B

⏭ Diagram :

✏ Please see the attached image for better understanding.

⏭ Calculation :

• Eq. of upper part

$\mapsto \sf \: C_1 = \frac{2C \times C}{2C + C} = \frac{2 {C}^{2} }{3C} \\ \\ \mapsto \sf \: \red{C_1 = \frac{2C}{3} }$

• Eq. of bottom part

$\mapsto \sf \: C_2 = \frac{2C \times C}{2C + C} = \frac{2 {C}^{2} }{3C} \\ \\ \mapsto \sf \: \blue{c2 = \frac{2C}{3}}$

• Net eq. capacitance

$\mapsto \sf \: C_{eq} = C_1 + C_2 = \frac{2C}{3} + \frac{2C}{3} \\ \\ \mapsto \sf \: \underline{ \boxed{ \bold{ \sf{ \purple{C_{eq} = \frac{4C}{3} }}}}} \: \star$