Level Three Capicitor question.

Discussion in 'Homework Help' started by elecstudentuk, Mar 11, 2012.

1. elecstudentuk Thread Starter New Member

Mar 11, 2012
1
0
Hello.
I need a bit of help on a specific part of a merit question related to capacitors, specifically charge.
A capacitor of 6.8 micro farads is connected in series with two parallel capacitors of 10 micro farads and 22 micro farads.
I have found the total circuit capcitance to be 5.608 micro farads ( using c1+(c2xc3/c2+c3) )
I have found the total charge to be 100.944 micro farads. To my understanding the charge of the capicitor orignally in series is equal to the total charge of the circuit. And to work out the charge of the capaictors in parallel i need to use the equation of -c x v = Charge on the specific capacitor.
However when i perform the calculations for c2 and c3 the charge i get for both of them combined exceeds the total circuit charge.....
Am i making a silly mistake here?

2. steveb Senior Member

Jul 3, 2008
2,431
468
Yes, you are.

Apr 5, 2008
19,550
3,984
4. mlog Member

Feb 11, 2012
276
36
First of all, you didn't mention the voltage applied to the total circuit. I'm assuming it is 18 volts, because you said the total circuit capacitance was 5.608 uF, to which I concur. However, the total capacitance is found by (6.8)(10+22)/[(6.8)+(10+22)] = 6.8*32/(6.8+32)=217.6/38.8 = 5.608 uF.

The charge is distributed in terms of the capacitance. For example, since the circuit is equivalent to 6.8 uF in series with a 32 uF, the charge across the 6.8 uF is 6.8/(6.8+32) = 0.1753 or 17.53% of the total charge. The charge across the parallel capacitors (32 uF) is 32/(6.8+32) = 0.825 or 82.5% of the total charge.

Therefore, if the total charge is indeed 100.944, then the charge across the 6.8 uF is 0.1753*100.944 = 17.7 Coloumbs, and the charge across the 32 uF is 0.825*100.944 = 83.3 Coloumbs. The charge across the 22 uF is 22*83.3/32 = 57.3 Coloumbs. The charge across the 10 uF is 10*83.3/32 = 26.0 Coulumbs.

Here's a summary.

17.7 Coloumbs for 6.8 uF
57.7 Coloumbs for 22 uF
26.0 Coloumbs for 10 uF
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101.4 Coloumbs Total (due to rounding error does not equal 100.944)