question about capacitance

[glidez28]

between points a and b, a 15uF capacitor and a 3uF capacitor are connected in a series, and then the two are connected in parallel with a 6uF capacitor. if the potential difference between a and b is 20V, how much charge is stored in each capacitor????

 

[glidez28]

.

 

[aphex]

wow, at times like these im glad im a Business Major

 

[glidez28]

it always looks hard when you're totally new to it, but in actuality, its not that bad

 

[Whitecloak]

is the equivalent capacitance 8.5uF?

 

[glidez28]

yeah..

 

[RossGr]

Capasitors in series add like resistors in parallel, capasitors in parallel add like resistors in series so..
for the 2 series caps we have

1/(1/3 + 1/15) = 15/6= 5/2 =2.5
now add on the parallel cap to get 8.5 microf.
The total charge is given by

Q= VC = 20 (8.5)

You can finish to get the final number. The total charge on the 6uF cap C=6 V=20
Use the total Capasitance of the series pair, C =2.5uF with V= 20V to get the total charge. The use the porportion of the 3:15 to find the charge on each.

 

[glidez28]

Rossgr, i understand that, but i need to find the charge in EACH capacitor. what do i do with the final Q?

 

[RossGr]

Yeah, I noticed that on a reread! I think I fixed it in an edit!

 

[OS]

"Use the total Capasitance of the series pair, C =2.5uF with V= 20V to get the total charge. The use the porportion of the 3:15 to find the charge on each."

Sorry Ross, I don't think you can do that. A property of series combination capacitors is that the charge on each capacitor must be the same. Convince yourself by using Q=CV and work backwards. Find the voltage across each series capacitor and add them up. The result should be 20V, which it must be or else Kirchoff's voltage law would be violated.


For the answer, I got

50 uC on the 15 uF cap

50 uC on the 3 uF cap

170 uC on the 6 uF cap

Again, convince yourself by using Q=CV, solve for the voltages, and reference them against 20 V. They should all be the same or else KVL was violated.

Someone drop kick me if I'm wrong.

 

[glidez28]

thanks guys!!!!

 

[RossGr]

Thanks for the fix outersquare, of course you are correct. The plates of the series caps that are tied together must have the equal charge, they are the same point afterall!