Download 3-28 Circuits, Current and Potential, Capacitors

Today 3/28
Circuits
Current
Potential (same as always)
Capacitance (energy and in circuits)
3/28 “Circuits 3”
Due Wednesday 4/2
Note: Watch out for “round off” errors,
keep three decimal places to the end on all
circuit homeworks.
HW:
Voltage Model
Voltage: how much energy each coulomb of
charge gains (battery) or loses (bulb) in
going through an element. (as usual)
More glow, more voltage.
The Loop Rule:
What goes up, must come down! VA,A = 0,
voltage rises and drops must must cancel
around any loop.
Current Model Fails
A
Compare B to D
B
less
current
C
1/
more D
current
2
all
B gets all of the current
through A. D gets half of the
current through C.
But the current through C is
bigger
than
the
current
throug
1/
2
E A.
Can’t be sure which is
brighter!!!
Voltage Model
A
V
think
loops
V
VA
VB
B
Compare B to D
Compare the voltages
across B and D. More
volts more glow! Recall
current for B and D.
C
VC
D
VD
C brighter than D
E C has more voltage than D
Voltage Model
A
in series
The voltage for series
elements SPLITS
because it adds up to
B the battery voltage.
The voltage splits
equally for identical Rs.
Otherwise, the voltage
drop is greater across
the greater R.
Find Equivalent Resistance
5
6
12 V
3
2
6
8 4 8
12 V
12
7
12
9
Req = 6
?
Find current through the battery
2
5
12 V
I = 2 Amps
6
8
8
12 V
7
9
It is the same as the
current through Req.
Req = 6
6
Current through each element
0.5 Amp
5
12 V
2 Amps
0.5 Amp
2
I = 2 Amps
6
8
8
12 V
1 Amp
7
0.25 Amp
each
1 Amp 9
What is the current through each resistor?
What is the voltage across each resistor?
6
Voltage across each element
12 V
5
5V
1V
2
3V
6
8
8
I = 2 Amps
12 V
2 V each
7
7V
9V
9
What is the current through each resistor?
What is the voltage across each resistor?
6
Kirchhoff’s Rules, Loop
The sum of all voltages around any
closed loop is zero. (what goes up must
come down)
or VA,A = 0
!!must keep track of ups and downs!! (+/-)
Kirchhoff’s Rules, Junction
The sum of all currents at any junction
is zero. (what goes in must come out)
!!must keep track of ins and outs!! (+/-)
Capacitors
Capacitance tells me how many coulombs of charge are
stored in a capacitor when it has 1 Volt across it.
A 25F capacitor will have 25C of charge on it when
it has 1 volt across it. Think of capacitance as
“coulombs per volt”.
Units:
coulombs per volt or “Farads”
Equation: C = q/V
Capacitors
Think of storing propane in a tank. The amount of
propane depends on the pressure just as the amount of
charge depends on voltage.
We will use parallel plate capacitors so that all ideas from
parallel plates apply.
V = Ed
E = /o (two plates)
 = Q/A
Capacitors
6F
How much charge is on the capacitor?
Think “6x10-6 Coulombs per Volt and you won’t need the
equation!
72x10-6 C or 72C
12 V
6F
Capacitors
6F
What is the E-field inside the capacitor if the plates have
an area of 1 m2?
Q = 72x10-6 C or 72C
Note that capacitance depends on
the area and separation distance
E = /o = 8.2x106 N/C
What is the distance between the plates?
12 V
6F
V = Ed
d = 12/8.2x106
= 1.5x10-6 m
Capacitors and Energy
How many Joules of energy are stored in the capacitor?
Ask yourself, “How much work must
be done to charge the plates?”
12 V
6F
Capacitors and Energy
How many Joules of energy are stored in the capacitor?
As the battery moves charge from one plate to another, the
potential difference increases from zero to 12 V. The average is
6 V and the energy stored is q times 6 V (qVave).
12 V
6F
Energy = qVave = 1/2qV = 1/2CV2
C = q/V
Capacitors with Resistors
Will current flow when the switch is closed?
Yes, but only for an instant until
the capacitor is charged.
12 V
6F
12 V
6
6F
Yes, but it will take longer to
charge the capacitor.
Capacitors with Resistors
Describe current and voltage long after the switch has
been closed.
No current, 12 V across the capacitor.
12 V
12 V
6F
Loop rule still applies!
V = IR for resistors still applies!
6
No current, 12 V across the capacitor,
zero V across the resistor.
6F
Capacitors with Resistors
Describe current and voltage long after the switch has
been closed.
2 Amps through the battery
and both resistors.
2
12 V
6F
4
Loop rule still applies!
V = IR for resistors still
applies!
4 V across 2 and 8 V across the
capacitor and 4
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Charging Capacitors in Series
The same amount of charge that enters one side of a
capacitor, leaves the other.
Capacitors in series
will always have
Current will
the same charge on
flow until the
them. (what goes
sum of the
around, comes
voltages across
around)
the capacitors
equals the
This is true even if
battery
they are not of
voltage.
equal capacitance!
(loop rule)
Capacitors in Series
Find the charge on each capacitor and the voltage across
each capacitor. The battery is 30V.
1
25F
2
50F
Q
C
V
They are in series so the charge on
each is the same.
Capacitance means “coulombs per
volt” so the one with twice the
capacitance has half the volts.
V1 = 20V, V2 = 10V, Q1 = 500C, Q2 = 500C
Capacitors in Parallel
Find the charge on each capacitor and the voltage across
each capacitor. The battery is 30V.
1
2
25F
50F
Q
C
V
They are in parallel so the voltage
across each is the same, each equal
to 30V.
Q1 = 750C, Q2 = 1500C
Series and Parallel
Objects in series have the same
current through them. This is why
capacitors in series always have the
same charge on them.
Objects in parallel have the same
voltage across them.
Ohm’s law, loops & junctions
V = IR true for entire circuits as well
as individual elements.
Voltage changes summed around any
closed loop equal zero.
Current divides and combines at
junctions like water in pipes. What
enters the junction must also leave.
Homework
100
R1=20
30F
15V
R1=20