AP Physics C: E&M. DC: Direct current. A constantly applied voltage causes charged particles to...
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Transcript of AP Physics C: E&M. DC: Direct current. A constantly applied voltage causes charged particles to...
INTRODUCTORY TERMSCurrent: Charge Flow. This is the drift of
electrons due to a potential difference.
AC: Alternating current. The polarity of the voltage source switches back and forth causing charges in
path to vibrate.DC: Direct current. A constantly applied
voltage causes charged particles to drift in one direction
Series: Elements in circuit are connected along one path.
Parallel: Elements of circuits are connected on separate branches.
CAPACITORS IN A DC CIRCUIT
+-
Voltage source
C1
C2
C3
Adding capacitors in series will lower the capacitance of the circuit when compared to the possible
capacitance of just one capacitor in the circuit.
Only the first plate of the first capacitor and the last plate of the last capacitor are actually connected to the voltage source, so only these plates will gain or lose electrons due to the potential difference of the
battery.
CAPACITORS IN A DC CIRCUIT
+-
Voltage source
C1
C2
C3
The inner plates are induced with charge. All capacitors carry an equivalent charge Q.
The voltage across all elements in the series will add up to that of the battery. Each capacitor has a different
capacitance and has the same charge, so the individual voltages will differ.
1 2 ... nV V V V
CAPACITORS IN A DC CIRCUIT
+-
Voltage source
C1
C2
C3
This should not be surprising since you are basically just making one big capacitor with a larger separation
(d).
Q is the same for all so the equivalent capacitance can be found with:
21
...eq n
Q Q Q Q
C C C C
21
1 1 1 1...
eq nC C C C
CAPACITORS IN A DC CIRCUIT
+-
Voltage source
C1
Adding capacitors in parallel will raise the capacitance of the circuit when compared to the possible
capacitance of just one capacitor in the circuit.
All capacitors are directly connected to the same voltage source so they will each reach the same
potential difference when charged.
C2 C3
CAPACITORS IN A DC CIRCUIT
Since each capacitor may have a different capacitance, each may hold a different amount of
charge, but the sum of the charge will equal that of one capacitor to replace those in parallel.
1 2 ... nQ Q Q Q
+-
Voltage source
C1 C2 C3
CAPACITORS IN A DC CIRCUIT
This should not be surprising since you are basically just making one big capacitor with a larger surface
area (A) for charge to be stored.
V is the same for all so the equivalent capacitance can be found with:
1 2 ...eq nC V CV C V C V
+-
Voltage source
C1 C2 C3
1 2 ...eq nC C C C
ELECTRIC CURRENT
It takes over 6.24 billion billion electrons to add
up to one coulomb!
1 C of charge through any cross section of wire per second is one AMP!
Electric current is the amount of charge passing through a certain area per second. It is measured in amperes.
ELECTRIC CURRENT
Iav Qt
If the charge flow rate varies, we define the
instantaneous current as:
IdQ
dt
The direction of current is the direction that positive charges would flow if free to do so.
n=number of charge carriers per unit volume A=cross-sectional area of wireΔx=length of section of wireΔQ=charge in a section of wireq=charge on each particle
Q nAx q
If charge carriers move with a velocity vd, then they move a distance Δx=vdΔt
ELECTRIC CURRENT
QnAv dtq
IQt
nAv dq
With no voltage, charges in a metal bounce around randomly similar to gas
molecules. With a voltage they still bounce around but slowly drift in one
direction.
DRIFT VELOCITY
A copper wire with cross-sectional area3x10-
6m2 carries a current of 10.0A. Find the drift speed of the electrons. The density of copper
is 8.95g/cm3.
DRIFT VELOCITY
from the periodic tableatomic mass of copper:
m=63.5g/mol
Vm
63.5g /mol
8.95g /cm3 7.09cm3 /mol
A copper wire with cross-sectional area3x10-
6m2 carries a current of 10.0A. Find the drift speed of the electrons. The density of
copper is 8.95g/cm3.
DRIFT VELOCITY
nnAV
6.021023electrons/mol
7.09cm3 /mol8.48x1022electrons/cm3
vd I
nqA
10A
8.48x1028electons/m3 1.6x10 19C 3x10 6m2
vd 2.46x10 4m/s
CURRENT DENSITY
We will define current density as:
JI
Anqvd
A current density J and an electric field E are established in a conductor when a
potential difference is maintained across the conductor.
The proportionality constant is called the conductivity of the conductor.
JE
OHM’S LAW
Named after Georg Simon Ohm (1787-1854)
For many materials, the ratio of the current density to the electric field is a constant,
(sigma), that is independent of the electric field producing the current.
If the potential difference is constant, the current is constant.
This is not a law of nature, but an empirical relationship found to be valid for certain
materials (most metals)
RESISTANCE AND TEMPERATURE:
0 1 T T0
R R0 1 T T0
For all metals, resistivity increases with temperature
increase.
some reference value usually at
20°C
Temperature coefficient of
resistivity
ELECTROMOTIVE “FORCE” – (EMF)An emf is any device (generator/battery)
that produces an electric field and thus may cause charges to move around in a circuit.
Is an emf (ε) any different than a voltage source (V)?
Any real emf has a certain amount of its own internal resistance, so the voltage that it will
supply to a circuit between terminals is slightly different than its own potential
difference.Both are measured in Volts.
ELECTROMOTIVE “FORCE” – (EMF)An emf can be thought of as a charge pump.
V Ir V is the terminal voltageEpsilon is the potential difference of the emfI is the circuit’s currentr is the internal resistance of the emfR is the equivalent resistance of the circuitP is the power dissipated in circuit and emf device
VIR
IR Ir
IR Ir
PI I2R I2r
KIRCHOFF’S RULES FOR COMPLEX CIRCUITS:
I am Bunsen. Have you tried my
burner?
The sum of the currents entering any junction must equal
the sum of the currents leaving that
junction.
The algebraic sum of the changes in
potential across all of the elements around any closed loop must
be zero.
KIRCHOFF’S RULES FOR COMPLEX CIRCUITS:
Do you mean that Energy and Charge are conserved?
Of course Bunsen,If charge is split
between two branches it must flow down one path. it will not build up in a location or
disappear.
Also, a charge must gain as much energy as it loses throughout the circuit because it begins and ends at
the same point.
By the way, nice burner!
RC CIRCUITSWhat is different about a circuit with a
resistor and a capacitor than one with just a resistor?
The current does not flow at a constant rate!
Why is this?
+-
The charge stops flowing when a capacitor matches the battery
voltage. It drains charge through the resistor after batter is
disconnected.
+++
-- - -
++++++
- - - - - - - -
C C RR
No current I
ΔVR=0 ΔVR=-IR
ΔVC=Q0/C ΔVC=Q/C
At time t=0 the switch is closed and the full capacitor discharges.
From the loop rule…
VC VR 0
Q
C IR 0
Q
C IR 0
IdQ
dt
Q
CdQ
dtR 0
Q and I are instantaneous values:
dQ
dt
Q
RC
dQ
Q
dt
RC
dQ
QQ0
Q
1
RCdt
0
t
lnQ
Q0
t
RC
eln
Q
Q0
e
t
RC
Q
Q0
et
RC