Full circuit containers many components:
• resistors (discussed last week)
• Capacitors and inductors (to be discussed this week)
• Op. Amps, Timers, etc (to be discussed next week)

Capacitors store energy in the form of an electric field
They tend to act like small secondary-cell batteries, being able to store and release electrical energy.

Resistor Capacitor (RC Circuit) : Switch in Off position
No
Voltage on
Capacitor
Capacitor
Plates
Dielectric
Plates
Switch
ON OFF
+
Battery
-
Resistor

Resistor Capacitor (RC Circuit) : Switch in On position
Capacitor becomes charged
To Voltage of the
Battery
Capacitor
------
Dielectric
++++
Switch
ON OFF
Electron flow
+
Battery
-
Resistor

Capacitor
Voltage (V)
Circuit
Current
(10 -4 A)

Charged
Capacitor
V Volts
Capacitor
------
Dielectric
++++
Switch
ON OFF
Electron flow
Resistor

Discharged
Capacitor
0 V
Capacitor
Dielectric
Switch
ON OFF
Electron flow
Resistor

Units for Capacitance
• Units of Capacitance are called Farads (F)
•Ability to hold charge called capacitance
Charge = Capacitance × Voltage
Q = C × V
• Current through capacitor proportional to rate of change in Voltage i =
!
Q
!
t
= C
!
V
!
t
• Inherent time scale is: τ = RC

Dielectrics and Capacitance
• A dielectric has several effects on a circuit.
1) A dielectric material responds to the presence of the electric field between the plates of a capacitor by reducing the voltage drop relative to empty space.
How? If you think of the atoms and molecules in a dielectric as small, shaped charges (and they are!), then you will find that they align themselves in along the field. This has the effect of creating an internal potential that acts to counter the one from the plates….
Since Q = C x V. Therefore, for a given Q, if V drops, then C must be HIGHER….
A dielectric thus increases the capacity of the system, or the amount of charge it holds!

Dielectrics and Capacitance
2) A dielectric material changes the response time of an
RC loop.
The time constant is t=RC. If R stays constant, but C is increased by using a dielectric, then t must increase as well!
3) A dielectric may permit a greater voltage to be put on the capacitor.
Air will only support so much voltage before it ceases to insulate and conducts…say as lightning .
Many dielectrics support larger voltage drops than air
(plexiglass will permit 15x as large a field…AND has 4x the ‘capacitance’).
Since Q = C x V, then increasing V stores more energy.

•Inductors store energy in the form of magnetic field
•Made up of coils of wire
•Sometimes the coils are wrapped around other material to increases its effect
•Response to applied voltage
•Or current different from capacitor

Inductors try to stop rapid changes in current through them
(1) Flip the switch ON Initially current cannot pass through inductor
Left on for a long time, current slowly builds in the inductor, while the bulb grows dimmer
(2) Flip the switch OFF
Light bulb would temporally grow brighter before going out

Circuit
Current (A)

Units for Inductance
• The unit of Inductance is a Henry (H)
• Inductance is the ability to store energy by using a magnetic field
• Voltage through inductor proportional to rate of change in current
V = L
!
I
!
t
• Inherent time scale is: τ = L/R

Capacitor
Voltage
(V)
Circuit
Current
(10 -4 A)
Circuit
Current
(A)
A Capacitor builds a potential from a current, while an Inductor builds current from a potential.

I
!
=
1
LC
I , Q

I
1
LC
I
!
=
Real Circuits all have some resistance….