#### Question

Take `C_1 = 4.0 "uF" and C_2 = 6.0 "uF"` in figure . Calculate the equivalent capacitance of the combination between the points indicated.

#### Solution

For the combination of capacitors given in figure (a), the pairs of capacitors *C*_{1}_{ }and *C*_{2}are in parallel.

The equivalent capacitance of each parallel combination of capacitors is given by*C*_{1}_{ }+ *C*_{2} = 4 + 6 = 10 μF

The equivalent circuit can be drawn as :

The equivalent capacitance for the above series circuit is given by

`1/C_(eq) = 1/(C_1 + C_2) + 1/(C_1+C_2) = 1/10 + 1/10 = 2/10`

⇒ `C_("eq") = 5 "uF"`

For the combination of capacitors given in figure (b), the pairs of capacitors *C*_{1}_{ }and *C*_{2}are in parallel.

The equivalent capacitance of each parallel combination of capacitors is given by*C*_{1}_{ }+ *C*_{2} = 4 + 6 = 10 μF

The equivalent circuit can be drawn as :

In the above circuit, it can be seen that C_{A }and C_{B} are in series and are in parallel to the series combination of C_{C }and C_{B}.

The equivalent capacitance for the series combination of C_{A }and C_{B }is given by

`1/C_(eq) = 1/C_A + 1/C_B = 1/(C_1+C_2) + 1/(C_1 + C_2)= 1/10 + 1/10 = 1/5`

⇒ `C_(eq) = 5 "uF"`

Similarly, the equivalent capacitance of the series combination of *C*_{C }and *C*_{D }is 5 μF.

∴ Net equivalent capacitance = 5 + 5 = 10 μF