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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? |
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Answer» `(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`. |
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