find the expression for the energy stored in the capacitor also find the energy lost when the charged capacitor - Physics - Electrostatic Potential And Capacitance

Question

find the expression for the energy stored in the capacitor also
find the energy lost when the charged capacitor is disconnected
from the source and connected in parallel with the uncharged
capacitor where does this loss of energy appear??

Aravind Subramanian · Answer

A charged Capacitor is a store of electrical potential
energy
To find the energy stored in a capacitor, let us consider a
capacitor of capacitance C, with a potential difference V between
the plates
There is a charge +q on one plate and –q on the other
Suppose the capacitor is charged gradually At any stage ,the
charge on the capacitor is q
Potential of capacitor =q/C
Small amount of work done in giving an additional charge dq to
the capacitor is
dW=q/C *dq
total work done in giving a charge Q to the capacitor is q
Q=Q
W=1/C Q2/2
Energy stored in the capacitor
U=W=1/2 Q2/C
Put Q=CV
U=1/2 (CV)2/C =1/2 CV2
Put CV=Q
U=1/2 QV
Thus, U=1/2 Q2/C =1/2 CV2=1/2 QV
When Q is in coulomb,V is in Volt ,C is in fared Energy U is in
joule
Energy stored in a capacitor is in the form of electric field
energy in the charged capacitor and it resides in the dielectric
medium between the plates

when lost
A charged Capacitor is a store of electrical potential
energy
To find the energy stored in a capacitor, let us consider a
capacitor of capacitance C, with a potential difference V between
the plates
There is a charge +q on one plate and –q on the other
Suppose the capacitor is charged gradually At any stage ,the
charge on the capacitor is q
Potential of capacitor =q/C
Small amount of work done in giving an additional charge dq to
the capacitor is
dW=q/C *dq
total work done in giving a charge Q to the capacitor is q
Q=Q
W=1/C Q2/2
Energy stored in the capacitor
U=W=1/2 Q2/C
Put Q=CV
U=1/2 (CV)2/C =1/2 CV2
Put CV=Q
U=1/2 QV
Thus, U=1/2 Q2/C =1/2 CV2=1/2 QV
When Q is in coulomb,V is in Volt ,C is in fared Energy U is in
joule
Energy stored in a capacitor is in the form of electric field
energy in the charged capacitor and it resides in the dielectric
medium between the plates

U = 1/2 A/4pi(s) (Es)^2 or E^2/8pi * volume

in the charge carriers
A charged Capacitor is a store of electrical potential
energy
To find the energy stored in a capacitor, let us consider a
capacitor of capacitance C, with a potential difference V between
the plates
There is a charge +q on one plate and –q on the other
Suppose the capacitor is charged gradually At any stage ,the
charge on the capacitor is q
Potential of capacitor =q/C
Small amount of work done in giving an additional charge dq to
the capacitor is
dW=q/C *dq
total work done in giving a charge Q to the capacitor is q
Q=Q
W=1/C Q2/2
Energy stored in the capacitor
U=W=1/2 Q2/C
Put Q=CV
U=1/2 (CV)2/C =1/2 CV2
Put CV=Q
U=1/2 QV
Thus, U=1/2 Q2/C =1/2 CV2=1/2 QV
When Q is in coulomb,V is in Volt ,C is in fared Energy U is in
joule
Energy stored in a capacitor is in the form of electric field
energy in the charged capacitor and it resides in the dielectric
medium between the plates

find the expression for the energy stored in the capacitor. also find the energy lost when the charged capacitor is disconnected from the source and connected in parallel with the uncharged capacitor. where does this loss of energy appear??