Capacitors in networks cannot always be grouped into simple series or parallel combinations. As an example, the figure shows three capacitors
,
, and
in a delta network, so called because of its triangular shape. This network has three terminals
,
, and
and hence cannot be transformed into a sinle equivalent capacitor.
The potential difference
must be the same in both circuits, as
must be. Also, the charge
that flows from point
along the wire as indicated must be the same in both circuits, as must
.
Now, let us first work with the delta circuit. Suppose the charge flowing through
is
and to the right. According to Kirchoff's first rule:
Lets play with the equation a little bit..
From Kirchoff's second law:
Therefore we get the equation:
![]() |
(1) |
We then get the second equation
![]() |
(2) |
Keeping these in mind, we proceed to the Y network. Let us apply Kirchoff's second law to the left part:
From conservation of charge,
Similarly for the right part:
The coefficients of corresponding charges in corresponding equations must be the same for both networks. i.e. we compare the equations for
Now compare the coefficient of
Substitute the expression we got for
Now we look at the coeffcient of
Again substituting the expression for
We have derived the required transformation equations mentioned at the top.
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