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Question: Find the value of the equivalent capacitance between \$a\$ and \$b\$ enter image description here

Solution:Because of the balanced bridge,so the circuit become

enter image description here

So \$C_{ab}=30 \mu //[(4\mu // 6\mu)+((6\mu // 9\mu))]=5\mu\$

Honestly,when i see there is a \$\Delta\$ circuit ,i will want to transform it to \$Y\$ circuit,i won't think about the "balanced bridged".so i want to ask :

  1. In what situation,we should consider the balanced bridged?i don't need to consider the balanced bridged when there are only two capacitors which they are parallel connected to each others.but why should i need to consider the balance bridged in this circuit?

2.Why will we ignore the \$5 \mu \$ capacitor,not the \$4 \mu \$ capacitor?

shineele
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    When the bridge is actually balanced. –  Apr 10 '20 at 09:54
  • @BrianDrummond But how do you know the bridge is actually balanced? can you explain this more? – shineele Apr 10 '20 at 10:19
  • There are 2 legs to the bridge. If you can confirm that the voltage at the midpoint of each leg is the same, the bridge is balanced. Then there is no voltage across the 5uF capacitor therefore no current through it and it has no effect. –  Apr 10 '20 at 10:42

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Term balanced bridge has been 150 years used for H-shaped circuit where the horizontal part has no voltage nor current because the left and right voltage dividers produce the same voltage. The idea was used originally in Wheatstone's resistance measurement bridge.

The same proportionality is true here; 4:6 = 6:9. If you consider 4uf, 6uF, 6uf and 9uF capacitors as impedances in an AC circuit you see their actions as two voltage dividers produce the same voltage. At all frequencies the omitted 5uF capacitor would have no current, it cannot be charged nor discharged. We can remove a current free part without affecting the rest of the circuit.

With different capacitor values general circuit calculation methods must be used. Y to delta transform can be used.

  • so you mean if i modify the \$4 \mu\$ capacitor to \$10 \mu\$,we can't ignore the \$5\mu\$ capacitor? – shineele Apr 10 '20 at 10:22
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    If the only change is to replace 4uF with 10uF the balance is lost and 5uF cannot be removed. –  Apr 10 '20 at 10:26