Question

40 pF capacitor is charged to 4 kV and then removed from the battery and connected in parallel to an uncharged 50 pF capacitor.

A.) What is the new charge on the second capacitor? Answer in units of nC

B.)
What is the new charge on the first capacitor?
Answer in units of nC
C.)
Find the change in energy.

For the life of me I can not figure out C if someone could please help me out

Answer 1

For part A I found the Charge on Q2 by using V=C1V1+C2V2/C1+C2 since V2 is 0 in this scenerio It reduced to C1V1/C1+C2 and Found V to be 1.77 kV
then found Q2 by Q2=C2V = 88.89 nC

For part B I used C1V1-88.9=71nc

Answer 2

Energy in a capacitor=q^2 /2C. Just apply the formula, you have found new charge dsitribution on both capcitors so final energy is (q1)^2/2c1+ (q2)^2/2c2. Similarly initial energy also you can find.
The formulae are E=1/2 CV^2= q^2/2C= QV/2

Answer 3

So I am suppose to do QV/2 - (q1)^2/2c1+ (q2)^2/2c2 = delta Energy? When I do this i get a negative number

Answer 4

That means energy reduces.

Answer 5

reduces by 10959 micro Jules?

Answer 6

Have you calculated charge correctly?
Initially Q=CV=160 + 10^something(Whatever units).
Now when you connect another capacitor. By charge conservation if q1 and q2 are new charges q1+q2=Q. And by kirchoff's Law you have q1/c1+ q2/C2=0. You can use these equations to find out q1 and q2.

Answer 7

But remember in capcitors energy is NOT conserved. While charging a capacitor then energy of a capacitor= 1/2 CV^2. But if you calculate work done by battery you will find it is exactly twice of the energy of capacitor even if wires have zero resistance. i.e, Wotk done by battery is CV^2. Which means 1/2 CV^2 energy is lost.

Answer 8

Yea i got Q= 160 nC or 160x10^-8 C
V= Q/C2 =1.77x10^3V
Q2=88.89X10^-8 C
Q1= 71.11 x 10^-8 C

Answer 9

then i used QV/2- [Q1^2/2C1+Q2^2/2C2]= Change in energy

Answer 10

Correct only then.

Answer 11

Correct only?

Answer 12

yeah...

Answer 13

Lol what do you mean by that?

Answer 14

i just said its correct :D

Answer 15

oh lol hmm when i type it is it says its wrong must be arithmetic on my part. Thanks for your help!