# confusion with getting Ct with a series circuit

Thread Starter

#### 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?

#### #12

Joined Nov 30, 2010
18,222
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. Thread Starter

#### 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. Thread Starter

#### 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

Or, better to calculate it all out in nanoFarads instead of microfarads (uF)

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

Try again

#### #12

Joined Nov 30, 2010
18,222
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
Thread Starter

#### james7701

Joined Jan 5, 2016
37
Unit issues

470 nF is equal to 0.47 uF

Or, better to calculate it all out in nanoFarads instead of microfarads (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
18,222

#### GopherT

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

Then take the reciprocal of that total to get your answer

#### #12

Joined Nov 30, 2010
18,222
Take reciprocal of c1 + reciprocal of C2

Then take the reciprocal of that total to get your answer
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.

Thread Starter

#### james7701

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

Thread Starter

#### james7701

Joined Jan 5, 2016
37

#### WBahn

Joined Mar 31, 2012
26,398
but, why are they showing an answer of 320?
Because that's the correct answer.

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!!!

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