Question

Find equivalent capacitance between points A and B. the answer will be C.

Answer 1

Let the capacitance $C_{AB}=x$

Now 2C and x are in series and then it is connected in parallel with C.

Thus, $C_{AB}=\frac{2Cx}{2C+x}+C=\frac{2Cx+2C^2+Cx}{2C+x}$

or $x=\frac{3Cx+2C^2}{2C+x}$

or $2Cx+x^2=3Cx+2C^2$

or $x^2-Cx-2C^2=0$

or $x^2+Cx-2Cx-2C^2=0$

or $x(x+C)-2C(x+C)=0$

or $(x+C)(x-2C)=0$

so $x=2C$ (negative value of capacitance invalid so it is neglected )