Answer to Question #101625 in Electricity and Magnetism for Yogesh Saini

Question

Determine the effective capacitance of the following combination of capacitors given
that the capacitance of each capacitor is 3 μF.

Answer 1

In a combination like this

the effective capacitance between A and B will be simply the sum of the capacities of all three capacitors:

$$C_0=C_1+C_2+C_3=\\=3C=3\cdot3\cdot10^{-6}=9\cdot10^{-6}\text{ F}.$$

If the capacitors were connected in series, the effective capacitance would be

$$\frac{1}{C_0}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}=\frac{3}{C},$$

$$C_0=C/3=1\space\mu\text{F}.$$

In a combination with series and parallel connections simplify the circuits applying these two rules.