Energy Stored in a Capacitor - Faculty Web...
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Energy Stored in a Capacitor z What is the potential energy, U, of a charged capacitor? z Think of U as being stored in E field between plates z Calculate W required to charge plates to potential V z Recover energy by discharging capacitor Vq W U Δ = = Δ
Transcript of Energy Stored in a Capacitor - Faculty Web...
Energy Stored in a Capacitor
What is the potential energy, U, of a charged capacitor?Think of U as being stored in E field between platesCalculate W required to charge plates to potential V
Recover energy by discharging capacitor
VqWU Δ==Δ
Energy Stored in a Capacitor
Charge capacitor by transferring electrons with a battery
More charge moved, E field between plates gets bigger, harder to move charges so takes positive work to charge capacitor
Energy Stored in a Capacitor
At given instance potential across plates is
Transfer increment of charge dq´, work required is
CqV′
=′
qdCqqdVdW ′′
=′′=qVW =
Energy Stored in a Capacitor
Work required from 0 to total charge q is
Potential energy = work
Or, use
Cqqdq
CW
q
21 2
0=′′= ∫
CqU2
2
=
2
21 CVU =CVq =
Energy Stored in a Capacitor
Advantage of capacitorGet more power than from just a battery
Slowly charge capacitor with battery and then discharge quicklyExamples – photo flash, medical defibrillator
2
21 CVU =
Capacitance
What if we have more than one capacitor in a circuit?
Replace combination with an equivalent capacitance
Two basic combinationsParallel Series
eqC
Capacitors in Parallel
Capacitors in parallelCapacitors are directly wired together at each plate and V applied across the group of plates
V is same across all capacitors
VVVV === 321
Capacitors in Parallel
Capacitors in parallelTotal q stored on capacitors is sum of the charges of all capacitors
Ceq has total charge qand same V as original capacitors
321 qqqq ++=
VqCeq =
Capacitors in Parallel
Capacitors in parallel
∑=n
iieq CC
VCq 11 = VCq 22 = VCq 33 =
321 CCCCeq ++=
321 qqqq ++=
( )VCCCq 321 ++=
Capacitors in Series
Capacitors in seriesCapacitors are wired one after the other and V is applied across the two ends of the seriesCapacitors have identical q
Battery produces q only on top and bottom plates, induced q on other plates
qqqq === 321
Capacitors in Series
Capacitors in seriesSum of V across all capacitors is equal to applied V
Ceq has same q and total Vas original capacitors
321 VVVV ++=
VqCeq =
Capacitors in Series
Capacitors in series
11 C
qV =2
2 CqV =
33 C
qV =
⎟⎟⎠
⎞⎜⎜⎝
⎛++=
321
111CCC
qV
⎟⎟⎠
⎞⎜⎜⎝
⎛++=
321
1111CCCC eq
321 VVVV ++=
Capacitors in Series
Capacitors in seriesCharge can only be shifted from one capacitor to another.
Ceq is always less than smallest capacitance
∑=n
i ieq CC11
Capacitors in Parallel & Series
Capacitors in parallelV across each is equalTotal q is sum
Capacitors in seriesq is equal on eachTotal V is sum
∑=n
iieq CC
∑=n
i ieq CC11
Capacitors in Parallel and Series
Capacitance (Exercise)
These are all the same
Capacitance (Exercise)
A battery with V stores total charge q on two identical capacitorsa) What is V across and q on either capacitor if they are in parallel?
• V is same for each and equal to V of battery.
• Total charge conserved and
121 2qqqq =+=2qqcap =
21 qq =
Capacitance (Exercise)
A battery with V stores charge q on two identical capacitorsb) What is V across and q on either capacitor if they are in series?
• q is same for each • V is sum of V across capacitors
121 2VVVV =+=2VVcap =
21 VV =
