Six capacitors of capacities `5muF,5muF,5muF,5muF,10muF` and X `muF` are connected in a network as shown in the figure. What is the value of X if the network is balanced?

Explanation

`(a)` The network will be balanced if DC arm has `5 mu F` capacity.
`:. (1)/(5)=(1)/(10)+(1)/(X)`
`(1)/(X)=(1)/(5)-(1)/(10)`
`(1)/(X)=(1)/(10)`
`X=10muF`.
`(b)` The network is balanced so, the `5 mu F` capacitor in arm BD car be neglected. Now, the equivalent capacitance `C_(1)` in arm ABC is
`(1)/(C_(1))=(1)/(5)+(1)/(5)=(2)/(5)`
`C_(1)=(5)/(2)muF`
Again, the equivalent capacitance `C_(2)` in arm ADC is
`(1)/(C_(2))=(1)/(5)+(1)/(10)+(1)/(10)=(4)/(10)`
`C_(2)=2.5muF`
Total capacity `=2.5+2.5=5 mu F`.