Download Unit 2 Day 3: Electric Energy Storage

Unit 2 Day 3: Electric Energy Storage
• Electric potential energy stored between capacitor
plates
• Work done to add charge to the capacitor plates
• Energy density of the electric field between
capacitor plates
• Movable parallel plate capacitor: change in electric
potential energy vs. work done to move plates
Energy Stored in a Capacitor
• A charged capacitor stores
electric potential energy in the
electric field between the plates
• The potential energy stored in the plates is
equivalent to the work done to charge the plates.
This work is usually done by a battery
• As charge is added to the plates, it takes
increasingly more work to add additional charge
because of electron repulsion
Energy Stored in a Capacitor
dU  V  dq or
dW   V  dq
Q
Q
2
1
q
Q
 W   V  dq   q  dq  12 |  12
C0
C 0
C
We can then say that the energy “stored” in the capacitor is:
Since Q  C  V
2


C


V
U1
2
C
2
2
Q
U  12
C
W (J)
 12 C V 
2
A
and V  E  d
d
Q (C)
A
then U  12  0 E 2  d 2  12  0 AdE 2 and u  12  0 E 2 is the energy density
d
Given C   0
Movable Parallel Plate Capacitor
+Q
-Q
A
The electric potential energy
decreases as the plates are
pulled apart
x
U  
+
ΔV
 0 AV 
2
3x
• The separation distance x, is increased to 3x, while the
battery remains connected
Movable Parallel Plate Capacitor
•
If the capacitor plate distance is increased with the
battery remaining connected:
–
–
–
–
–
–
•
ΔV is constant
A
C 
Capacitance decreases
d
Charge decreases Q  C  V
E decreases E  lV
Ue stored, decreases U   A  d  E
Energy density decreases u   E
0
e
1
2
2
0
1
2
2
0
If the capacitor plate distance is increased with the
battery removed:
–
–
–
–
–
–
Charge is constant
A
Capacitance decreases C   d
Q
V 
ΔV increases
C
Q
E is unchanged E   A
Ue stored, increases U   A  d  E
Energy density is unchanged u 
0
0
e
1
2
2
0
1
2
0E2