A 4 micro farad capacitor charged by 200 volt supply It is then dissconnected from the supply and is - Physics - Electrostatic Potential And Capacitance

Question

A 4 micro farad capacitor charged by 200 volt supply It is then
dissconnected from the supply and is connected to anothe uncharged
2 micro farad capacitor How much electrostatic energy of first
capacitor is lost in the form of heat or e m radiations?

Somnath physics · Accepted Answer

Here,

C1 = 4 Î¼F = 4
Ã—10-6F

V1 = 200 volt

C2 = 2 Î¼F = 2
Ã—10-6F

V2 = 0

Initial Electrostatic energy stored in the capacitors will
be

Ui = Â½
C1V12 + Â½
C2V22

=>Ui = Â½ Ã—4
Ã—10-6 Ã— (200)2 +
0 = 8Ã—10-2J

After connecting the two capacitors, the total capacitance
becomes

C = C1 + C2 = 4
Ã—10-6 + 2 Ã—10-6 =
6Ã—10-6 F

Charge in the first capacitor

Q = C1V1

=> Q = 4 Ã—10-6Ã—200 =
8Ã—10-4 C

Since, the 2nd capacitor is uncharged so total charge on
the system will be Q = 8Ã—10-4 C

Let V be the common potential of the capacitors after
connection

V = Q/C

=> V =
8Ã—10-4/6Ã—10-6 =
4/3Ã—102 volt

Now final electrostatic energy of the combination will
be

Uf = Â½CV2 =
Â½Ã—6Ã—10-6Ã—(4/3Ã—102)2
= 4Ã—10-2 J = 5
33Ã—10-2 J

Now loss in energy in form of heat etc will be

Ui - Uf = (8-5 33)
Ã—10-2 J = 2 67
Ã—10-2J

A 4 micro farad capacitor charged by 200 volt supply. It is then dissconnected from the supply and is connected to anothe uncharged 2 micro farad capacitor. How much electrostatic energy of first capacitor is lost in the form of heat or e. m radiations?