# confusion with getting Ct with a series circuit

#### james7701

Joined Jan 5, 2016
37
ok so, the first problem i was able to apply the formula to get my answer but, the 2nd problem i don't understand why im not getting the answer. (which is 320 )
any suggestions as of different approach to this?

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#### #12

Joined Nov 30, 2010
18,210
The answer isn't 320 as far as I can tell. I see 470 uf in series with 1 uf, and the answer to 2 caps in series is always less than the smallest capacitor. I see .9978769 uf on my calculator.

Still, I prefer a method that can do more than 2 capacitors, so don't get too invested in this formula. It's right for 2 caps, but life serves up different problems eventually.

#### james7701

Joined Jan 5, 2016
37
The answer isn't 320 as far as I can tell. I see 470 uf in series with 1 uf, and the answer to 2 caps in series is always less than the smallest capacitor. I see .9978769 uf on my calculator.

Still, I prefer a method that can do more than 2 capacitors, so don't get too invested in this formula. It's right for 2 caps, but life serves up different problems eventually.

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#### james7701

Joined Jan 5, 2016
37
but, why are they showing an answer of 320?

#### GopherT

Joined Nov 23, 2012
8,012
Unit issues

470 nF is equal to 0.47 uF

So, 1uF = 1000 nF in series with 470 nF

Try again

#### #12

Joined Nov 30, 2010
18,210
It's the units labels that went wrong. You have to convert 1 uf to 1000 nf to get the formula to work.

#### GopherT

Joined Nov 23, 2012
8,012

#### james7701

Joined Jan 5, 2016
37
Unit issues

470 nF is equal to 0.47 uF

So, 1uF = 1000 nF in series with 470 nF

Try again
so, i do 470÷1000 and 471÷1000?

#### #12

Joined Nov 30, 2010
18,210
(470 x 1000) /(470+1000)

#### GopherT

Joined Nov 23, 2012
8,012
Take reciprocal of c1 + reciprocal of C2

#### #12

Joined Nov 30, 2010
18,210
Take reciprocal of c1 + reciprocal of C2

That's the formula I was trying to think of in post #2. You can add up the 1/x's all day long, then 1/x the result to get the answer.

#### james7701

Joined Jan 5, 2016
37
(470 x 1000) /(470+1000)
so, it's best to change the units? and than proceed?

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#### james7701

Joined Jan 5, 2016
37

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#### WBahn

Joined Mar 31, 2012
25,925
but, why are they showing an answer of 320?

If you track your units, you would have seen where you went wrong.

$$\frac{470 \, nF \, \times \, 1 \, \mu F}{470 \, nF \, + \, 1 \, \mu F}$$

Now when you look at the denominator you don't see 470 + 1, you see two things that can't be added together that way because they don't have the same units.

$$\frac{470 \, nF \, \times \, 1 \, \mu F}{0.470 \, \mu F \, + \, 1 \, \mu F}$$

NOW you can add the denominator

$$\frac{470 \, (nF)(\mu F)}{1.470 \, (\mu F)}$$

Now the uF cancel, leaving you with 320 nF.

Always, always, ALWAYS track your units!!!