Book Reference : Pages 96-97Book Reference : Pages 96-97

1.1. To understand that when a capacitor is To understand that when a capacitor is charged it stores energycharged it stores energy

2.2. To be able to calculate the amount of energy To be able to calculate the amount of energy storedstored

3.3. To be able to solve problems involving the To be able to solve problems involving the energy stored in a capactitorenergy stored in a capactitor

We have seen from last lesson that when capacitor is We have seen from last lesson that when capacitor is charged, the pd across the plates increases in proportion charged, the pd across the plates increases in proportion to charge.to charge.

Charge on plates / C

Plat

e pd

/ V

V

Q

v

q q + q

Consider one step in Consider one step in the charging process a the charging process a capacitor from q to q + capacitor from q to q + q. q.

Work must be done to Work must be done to force the extra charge force the extra charge onto the plates & this onto the plates & this can be given bycan be given by

E = vE = vqq

Where v is the average Where v is the average voltage during this voltage during this stepstep

The work done in this small step from charging from q to The work done in this small step from charging from q to q + q + q is shown by the green vertical strip in the graphq is shown by the green vertical strip in the graph

Charge on plates / C

Plat

e pd

/ V

V

Q

v

q q + q

If we consider all the If we consider all the steps from a pd of 0 to steps from a pd of 0 to a the full pd of V then a the full pd of V then the energy stored is the energy stored is given by the area given by the area under the graph.under the graph.

This can be calculated This can be calculated from ½ base x heightfrom ½ base x height

Energy stored = Energy stored =

E= ½QV E= ½QV

The energy equation :The energy equation :

E= ½QVE= ½QV

Can be re-written in alternative forms...Can be re-written in alternative forms...

Since Q = CVSince Q = CV

Substitute for Q : E= ½CVSubstitute for Q : E= ½CV22

OrOr

Substitute for V : E= ½QSubstitute for V : E= ½Q22 / C / C

Doubling the charge also doubles the pd (voltage) Doubling the charge also doubles the pd (voltage) & vice versa. If we look at the & vice versa. If we look at the

E= ½CVE= ½CV22

Form of the equation we can see that this will Form of the equation we can see that this will quadruple the energy storedquadruple the energy stored

While charging the power supply (battery) While charging the power supply (battery) transfers energy equal to QV. Half of this energy transfers energy equal to QV. Half of this energy is stored in the capacitor (E= ½QV) the other half is stored in the capacitor (E= ½QV) the other half is wasted through the resistance in the circuit is wasted through the resistance in the circuit and dissipated to the surroundings as heat and dissipated to the surroundings as heat

Calculate the charge and the energy stored if a 10 Calculate the charge and the energy stored if a 10 F capacitor is charged to F capacitor is charged to

3.0V and 6.0V3.0V and 6.0V

[30[30C & 45C & 45J, 60J, 60C & 180C & 180J]J]

In the following circuit a charged capacitor with In the following circuit a charged capacitor with value C is allowed to discharge through a light value C is allowed to discharge through a light bulb. bulb.

V

Switch

Charge Discharge

JoulemeterIn Ou

t

Readings :Readings :

1.1.Charge the capacitor, read Charge the capacitor, read the pd and the initial the pd and the initial joulemeter readingjoulemeter reading

2.2.Discharge the capacitor & Discharge the capacitor & take a further joulemeter take a further joulemeter readingreading

C

Results :Results :

Compare the difference Compare the difference between the two joulemeter between the two joulemeter readings with E= ½CVreadings with E= ½CV22

+ + + +

- - - -

During a storm the cloud During a storm the cloud and the Earth below act and the Earth below act like a pair of charged like a pair of charged plates & a strong electric plates & a strong electric field existsfield exists

If the cloud and ground are separated by d, then If the cloud and ground are separated by d, then then potential difference V is given by : then potential difference V is given by :

V = EdV = Ed

Where E is the electric field strengthWhere E is the electric field strength

For a cloud carrying a charge of Q then the For a cloud carrying a charge of Q then the energy is given by ½QV which can be expanded energy is given by ½QV which can be expanded to ½QEdto ½QEd

If the wind moves the cloud to a new height d’ If the wind moves the cloud to a new height d’ then the new energy stored will be ½QEd’then the new energy stored will be ½QEd’

Note : The electric field strength E remains unchanged since it Note : The electric field strength E remains unchanged since it depends on charge per unit areadepends on charge per unit area

The increase in energy is given by ½QEd’ - ½QEdThe increase in energy is given by ½QEd’ - ½QEd

We can rewrite this as ½QEWe can rewrite this as ½QEd where d where d = d’ – dd = d’ – d

This increase in stored energy has come from This increase in stored energy has come from the work done by the wind overcoming the the work done by the wind overcoming the electrical attraction between the cloud and electrical attraction between the cloud and Earth which have opposite charges Earth which have opposite charges

The insulating properties of air break down The insulating properties of air break down when the field strength reaches more than when the field strength reaches more than about 300kV/mabout 300kV/m

A 50,000A 50,000F capacitor is charged from a 9V F capacitor is charged from a 9V battery and then discharged through a battery and then discharged through a light bulb in a flash which lasts 0.2s. light bulb in a flash which lasts 0.2s. Calculate :Calculate :

The charge and energy stored before dischargeThe charge and energy stored before discharge

The average power supplied to the light bulbThe average power supplied to the light bulb

[0.45C & 2J, 10W][0.45C & 2J, 10W]