Derive energy stored by a charged capacitor is half cv square
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Answer:
Explanation:(a)
Power across capacitor is P=VI
P=V
dt
dQ
By definition of capacitance, Q=CV
Pdt=
C
Q
dQ
Energy stored is
U=∫Pdt=
2C
Q
2
...........(i)
Electric field inside the capacitor is given by:
E=
ε
o
σ
=
Aε
o
Q
Capacitance C=
d
ε
o
A
Q=ECd.........(ii)
Substituting (ii) in (i),
U=
2C
E
2
C
2
d
2
=
2
E
2
ε
o
Ad
Energy density
Ad
U
=
2
1
ε
o
E
2
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