Homework Help: Potential Difference across capacitors in parallel.

1. Jul 31, 2011

OUmecheng

1. The problem statement, all variables and given/known data

Two capacitors, C1 = 20 micro Farads and C2 = 5 Micro Farads are connected in parallel and the resulting combination is connected to a 12-V battery. Find (a) the Equivalent capacitance of the combination, (b) the electric charge on each capacitor, (c) the potential difference across each capacitor, and (d) the energy stored in each capacitor.

2. Relevant equations

Ceq = C1 + C2

Q = CV

Ec = QV/2 = (C(V^2))/2 = (Q^2)/2C

3. The attempt at a solution

(a) 2.0x10^-6 F + 5x10^-6 F = 2.5x10^-5 F

(b) Q = CV,

Q1 = (20x10^-6 F)(12V) = 2.4x10^-4 C

Q2 = (5x10^-6 F)(12V) = 6x10^-5 C

(c) Not quite sure what this is asking for?

(d) Ec = CV^2/2

Ec1 = c1V^2 / 2 = 0.00144 F*V^2

Ec2 = c2V^2 / 2 = 3.6x10^-4 F*V^2

As you can see I've worked most of this out, seems simple enough, but I dont know what to do for (c)?

2. Jul 31, 2011

kuruman

It's simpler than you think. Draw yourself the circuit and look at it.

3. Jul 31, 2011

OUmecheng

errrr charge over capacitance?

Last edited: Jul 31, 2011
4. Jul 31, 2011

kuruman

How did you do part (b)? What voltage did you assume across each capacitor?

5. Jul 31, 2011

kuruman

Please don't edit previous posts. Just post a new response.

Your "attempt at a solution for (b) says

(b) Q = CV,

Q1 = (20x10^-6 F)(12V) = 2.4x10^-4 C

Q2 = (5x10^-6 F)(12V) = 6x10^-5 C

Tell me in English what do the numbers highlighted in red represent?

6. Jul 31, 2011

OUmecheng

Battery Voltage/Potential Difference?

7. Jul 31, 2011

kuruman

It is not a ratio. In plain English the equation Q = CV means

The charge on a capacitor is the same as the capacitance multiplied by the potential difference (or voltage) across the terminals of the capacitor.

8. Jul 31, 2011

OUmecheng

So the potential difference is the same as charge on a capacitor divided by the capacitance.

V1= Q/C1
V2= Q/C2

Thanks!

9. Jul 31, 2011

kuruman

Actually, you are doing it backwards. Memorize this definition

"Two circuit elements in parallel share the same potential difference (or voltage) across their terminals"

and use it constructively.

Cheers.