Download LECTURE.2.Electricity

LECTURE 2: BASIC PRINCIPLES OF ELECTRICITY
REQUIRED READING: Kandel text, Appendix Chapter I
Neurons transmit electrical currents
Behavior of synaptically linked neurons has similarities to
behavior of solid-state electrical circuits
Therefore, a fundamental appreciation of the nervous system
requires understanding its electrical properties
THIS LECTURE INTRODUCES BASIC CONCEPTS, TERMINOLOGY,
AND EQUATIONS OF ELECTRICITY ESSENTIAL TO OUR
TACKLING THE ELECTROPHYSIOLOGY OF NEURONS AND
NEURAL CIRCUITS
CHARGED PARTICLES AND ELECTROSTATIC FORCE
Some particles have electrical CHARGE; charge can be POSITIVE or NEGATIVE
Charged particles exert FORCE on each other:
LIKE charges REPEL
OPPOSITE charges ATTRACT
{examples of charged particles: electrons (-), ions (- OR +)}
+
-
+
NEUTRAL
FORCE
+ +
+
-
POSITIVE
+ +
+
POSITIVE
-
+
FORCE
+
REPULSIVE
NO
FORCE
+
ATTRACTIVE
Force experienced by charged particle determined by the sum and distances
of surrounding charges
+
- +NEGATIVE
- +-
NEGATIVE
ELECTRICAL CONDUCTANCE AND RESISTANCE
A
WHEN CHARGED PARTICLES ARE SUBJECT TO
ELECTRICAL FORCE, THEIR ABILITY TO MOVE
+ +
+
FROM POINT A TO B IS INFLUENCED BY
CONDUCTIVE PROPERTY OF MATERIAL
POSITIVE
-
+
CONDUCTANCE (g) {units=siemens,S}
measure of material’s ease in allowing
movement of charged particles
B
RESISTANCE (R) {units=Ohms,W}
measure of material’s difficulty in allowing
electrical conduction
Resistance is the INVERSE of Conductance. I.e.:
R=
1
g
OR
g= 1
R
- +-
NEGATIVE
VOLTAGE AND CURRENT
When there is a charge differential between two
points, energy is stored. This stored energy is
called ELECTRICAL POTENTIAL or
VOLTAGE DIFFERENTIAL (DV)
{units = volts, V}
VA
A
+ +
+
POSITIVE
-
DV = VA - VB
When there is a voltage differential between two
points in a conductive material, charged particles
will be forced to move. Movement of charge is
an ELECTRICAL CURRENT
CURRENT (I) {units = amperes, A}
is the RATE of charge flow.
I = dq / dt
DV
B
+
- +VB
I
NEGATIVE
Where q = amount of charge {units = coulombs, Q}
and t = time {units = seconds, s}
NOTE: I > 0 means net flow of positive charge; I < 0 means net flow of negative charge
OHM’S LAW
The amount of current flow is directly proportional to both
the voltage differential and the conductance
I = DV x g
Since g = 1 / R
I = DV / R
OR
DV = I x R
WATER PRESSURE ANALOGY
SCHEMATIC DIAGRAM
I
VA
VB
VALVE
PA
FLOW RATE
PB
R
DV = VA - VB = IR
I = DV / R
Water Pressure is analogous to Voltage Differential
Valve Resistance is analogous to Electrical Resistance
Flow Rate is analogous to Electrical Current
Flow Rate = Water Pressure / RVALVE
THE “I-V PLOT” & OHM’S LAW
I
VA
I = DV x g
VB
R
CONDUCTANCE ( g )
is SLOPE
of line in
I - V PLOT
In a simple resistive circuit, the relationship
between current and voltage is LINEAR
- 20
I
I
20
20
10
10
- 10
- 10
10
20
- 20
HIGH CONDUCTANCE
DV
- 20
- 10
- 10
10
20
DV
- 20
WEAKER CONDUCTANCE
MULTIPLE RESISTANCES IN SERIES
IN SERIES RESISTANCES SUM TO GIVE OVERALL RESISTANCE
POSITIVE
a
R1
b
R2
I1
I2
DV1
DV2
c
NEGATIVE
Two resistances are summed
to give the overall resistance
between points a and c
RTOTAL (a,c) = R1 (a,b) + R2 (b,c)
Currents are equal along
the series
ITOTAL (a,c) = I1 (a,b) = I2 (b,c)
By Ohm’s Law, the total voltage
differential equals the sum of
the component voltages
DVTOTAL (a,c) = DV1 (a,b) + DV2 (b,c)
MULTIPLE RESISTANCES IN PARALLEL
R1
I1
POSITIVE
ITOTAL
I2
Total current is the sum of individual
parallel currents
Total conductance is the sum of
parallel conductances
The voltage differential between two points
is the same no matter what the path
By Ohm’s Law, larger current travels thru
the “path of least resistance”
NEGATIVE
R2
ITOTAL = I1 + I2
gTOTAL
=
g1
+
g2
DVTOTAL = DV1 = DV2
I1 x R1 = I2 x R2
CIRCUIT DIAGRAM
POSITIVE
ITOTAL
I1
R1
I2
R2
EQUIVALENT
REPRESENTATIONS
I1
I2
ITOTAL
+
R1
R2
ITOTAL
NEGATIVE
+
-
SYMBOL DESIGNATES A VOLTAGE GENERATOR (POWER SOURCE)
WHICH MAINTAINS A CHARGE DIFFERENTIAL FROM ONE SIDE
TO THE OTHER (e.g. A BATTERY)
BEHAVIOR OF A SIMPLE RESISTIVE CIRCUIT
SWITCH OPEN
AT t = 0 sec
SWITCH CLOSED
AT t = 5 sec
I
I
+
R
DV
(10 W )
-
10 V
+
R
DV
(10 W )
-
I (Amps)
DV (volts)
CIRCUIT PROPERTIES
10
0
1
0
0
5
t (sec)
0
5
t (sec)
10 V
CAPACITANCE
SOME MATERIALS CANNOT CONDUCT ELECTRICITY, BUT CAN ABSORB CHARGE
WHEN SUBJECTED TO A CURRENT OR VOLTAGE
CAPACITANCE (C) {units = farads , F}
is the measure of the AMOUNT OF CHARGE DIFFERENTIAL which builds up
ACROSS a material when subjected to a voltage differential.
q = DV x C
or
DV = q / C
I.e. Larger capacitance ----> Larger charge stored
A material that has capacitance is called a capacitor. The schematic symbol for a
capacitor is:
C
BEHAVIOR OF A SIMPLE CAPACITIVE CIRCUIT
SWITCH OPEN
AT t = 0 sec
SWITCH CLOSED
AT t = 5 sec
I
I
+
DV
C
-
(10 F )
+
10 V
C
DV
-
(10 F )
Q (coulombs)
I (Amps)
DV (volts)
CIRCUIT PROPERTIES
10
0
100
0
0
5
t (sec)
0
5
t (sec)
0
0
5
t (sec)
10 V
RELATIONSHIP OF CAPACITANCE AND CURRENT
AS DESCRIBED BEFORE:
q = C x DV
SINCE
I = dq /dt
dq/dt = I = C x dDV/dt
I.e. As current flows into a capacitor, the voltage across it increases
CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES
SWITCH OPEN
BEFORE t = 0
SWITCH CLOSED
AT t = 0 sec
I
R
I
+
DVA
(5 W )
-
R
10 V
DVA
(5 W )
DVB
C
-
DVB
C
(1 F )
+
(1 F )
( REMEMBER: After switch closed, DVA + DVB = DVTOTAL = 10 V )
10
0
-5
0
5
t (sec)
10
10
I (amps)
DVB (volts)
DVA (volts)
CIRCUIT PROPERTIES
0
-5
0
5
t (sec)
10
2
0
-5
0
5
t (sec)
10
10 V
LOGARHYTHMIC DECAY OF CURRENT THROUGH A
CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES
SWITCH OPEN
SWITCH CLOSED AT
BEFORE t = 0
t = 0 sec
I
I
R
DVA
C
DVB
(5 W )
+
-
R
10 V
(5 W )
C
-
DVB
10 V
(1 F )
(1 F )
Equ. A
+
DVA
d VC
I=C
dt
Equ. B
VR
VTOT - VC
I=
=
R
R
Combine equations A & B and integrate
VC (t) = VTOT (1 - e t / RC
V (t) = V
e t / RC
R
TOT
(
)
)
As capacitor charges, VR and I decay logarhythmically
CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES
CONTROL OF CURRENT FLOW BY SIZE OF R AND C
SWITCH OPEN
SWITCH CLOSED
I
R
C
I
DVA
DVB
+
R
C
DVA
+
-
DVB
THE LARGER THE RESISTANCE (R) ---->
THE SMALLER THE INITIAL CURRENT SIZE
THE LONGER IT TAKES FOR CAPACITOR TO CHARGE
THE SLOWER THE DECLINE IN CURRENT FLOW
THE LARGER THE CAPACITANCE (C) ----> THE LONGER IT TAKES FOR CAPACITOR TO CHARGE
THE SLOWER THE DECLINE IN CURRENT FLOW
NO EFFECT ON INITIAL CURRENT SIZE
t1/2-max (sec) = 0.69 x R (W) x C (F)
CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES
CHARGE AND DISCHARGE OF A CAPACITOR
CHARGE SWITCH CLOSED AT t = 0 sec
CHARGE SWITCH OPENED AT t = 10 sec
DISCHARGE SWITCH CLOSED AT t = 10 sec
I
R
+
DVA
(5 W )
C
10 V
-
DVB
(1 F )
CIRCUIT PROPERTIES
0
-10
10
DVB (volts)
2
RESISTOR
VOLTAGE
I (amps)
DVA (volts)
10
0
-2
0
5
10
t (sec)
15
20
0
CAPACITOR
VOLTAGE
-10
0
5
10
t (sec)
15
20
0
5
10
t (sec)
15
20
CIRCUIT WITH CAPACITANCE & RESISTANCE IN PARALLEL
DVA (volts)
SWITCH OPEN BEFORE t = 0 sec
SWITCH CLOSED AT t = 0 sec
ITOT
(5 W )
-
IB
RB
(5 W )
-5
0
5
10
t (sec)
C
ITOT
(1 F )
0
10 V
IC
DVB
5
+
DVA
I TOT (amps)
RA
10
2
1
0
-5
0
5
10
1
0
-5
0
5
t (sec)
10
10
I B (amps)
2
DVB (volts)
I C (amps)
t (sec)
5
0
-5
0
5
t (sec)
10
2
1
0
-5
0
5
t (sec)
CURRENT FLOW
THROUGH
PARALLEL
RESISTOR
IS DELAYED
BY THE
CAPACITOR
{
10
CIRCUITS WITH TWO BATTERIES IN PARALLEL
+
IB
RB
-
+
VB
VA
I B (amps)
SWITCH CLOSED AT t = 0 sec
0
-5
0
-
VA = VB + IBRB
In this circuit,
what is VC at steady state?
(eq.1)
also
or
RB
+
VB
-
10
RA
IA
+
IA + IB + IC = 0
VA
CONCLUSION:
-
IC
VC
/
IB = (VA - VB) RB
VC = VA + IARA = VB + IBRB
therefore, (eq.2)
IB
5
t (sec)
and
IC = 0
IA = - IB
Combining eq. 1 & 2, and converting R to g
VC =
VA gA + VB gB
gA + gB
VC is the weighted average of the two batteries,
weighted by the conductance through each battery path
RESISTANCES & CAPACITANCES ALONG AN AXON
ION
CHANNEL (g)
MEMBRANE (C)
CYTOSOL (g)
Lipid bilayer of plasma membrane is NONCONDUCTIVE, but has CAPACITANCE
Ion channels in membrane provide sites through which selective ions flow,
thereby giving some TRANSMEMBRANE CONDUCTANCE
Flow of ions in cytosol only limited by diameter of axon; the WIDER the
axon, the greater the AXIAL CONDUCTANCE
MODELLING THE AXON AS RESISTANCES & CAPACITANCES
RM
CM
RM
RAXON
RAXON
CM
RM
CM
RAXON
RAXON
The axon can be thought of as a set of segments, each having an
internal axon resistance in series with a transmembrane
resistance and capacitance in parallel
When a point along the axon experiences a voltage drop across
the membrane, the SPEED and AMOUNT of current flow down
the axon is limited by RAXON, RM, and CM.
IM1
IA1
IC1
IA2
Axon current nearest the voltage
source (IA1) does not all proceed
down the axon (IA2). Some current
is diverted through membrane
conductance (IM1), and current
propogation down axon is delayed
by diversion into the membrane
capacitance (IC1).
+
Next lecture: ION CHANNELS & THE RESTING MEMBRANE POTENTIAL
REQUIRED READING: Kandel text, Chapters 7, pgs 105-139