0
\$\begingroup\$

Homework: I am trying to wrap my head around converting a capacitor circuit into an equivalent capacitor. I have looked at resources saying that it is the same as delta-wye transformation of resistors, but in reverse. I thought I had the process right, but I keep getting the wrong answer.

      24       48
a-----)|---o---|(---o
           |\       |
           | \ 4    |
        8 |(  |(   |( 24
           |    \   |
           |     \  |
           |      \ |
b-----|(---o---)|---o
      10       30

I combined the 48 and 24 into one, then took a Delta-wye transform:

      24        16
a-----)|---o----|(----o
            \        /
             \      /
          C2 |(    )| C3
               \  /
                \/
                o
                |
               |( C1
                |
b-----|(--------o
      10

The calculations I used were as follows:

4*8 + 4*30 + 8*30 = 392

C1 = 392/4 = 98

C2 = 392/30 = 13.1

C3 = 392/8 = 49

Plugging in those numbers the equivalent capacitance should be:

Ceq = (24^-1 + 98^-1 + 10^-1)^-1 + 13.1 + (16^-1 + 49^-1)^-1 = 31.7

Unfortunately this is the wrong answer. I'm not sure what i'm doing wrong, Please help.

\$\endgroup\$
1
  • 3
    \$\begingroup\$ I don't see any need for D-Y here. \$\endgroup\$ – user_1818839 Jul 19 '15 at 22:01
2
\$\begingroup\$

Allow me to draw it in a different way:

Circuit Rearranged

Now have another go at solving the problem.

A final hint: You will need to use the following two equations a total of 5 times (one equation is used twice, and the other three times).

$$\frac{1}{C_{series}} = \frac{1}{C_{1}} +\frac{1}{C_{2}} +...$$

$$C_{parallel} = C_1+C_2+...$$

\$\endgroup\$
3
  • \$\begingroup\$ p.s. the answer starts with a 5. But that's all I'm saying ;) \$\endgroup\$ – Tom Carpenter Jul 19 '15 at 23:04
  • \$\begingroup\$ Wow, I definitely made it more complicated than needed. Thank you @TomCarpenter. \$\endgroup\$ – Mark Walsh Jul 19 '15 at 23:35
  • \$\begingroup\$ I also see where I made a mistake in my Ceq. It should have been: Ceq = 1/(1/24 + 1/10 + 1/98 + 1/(13.1+1/(1/16+1/49))) Which also equals the answer. \$\endgroup\$ – Mark Walsh Jul 19 '15 at 23:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.