Title: LECTURE 2: BASIC PRINCIPLES OF ELECTRICITY
1LECTURE 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 solidstate 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
2CHARGED 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 ) Force experienced
by charged particle determined by the sum and
distances of surrounding charges
ATTRACTIVE FORCE
REPULSIVE FORCE
NO FORCE
NEUTRAL
POSITIVE
NEGATIVE
3ELECTRICAL CONDUCTANCE AND RESISTANCE
WHEN CHARGED PARTICLES ARE SUBJECT TO ELECTRICAL
FORCE, THEIR ABILITY TO MOVE FROM POINT A TO B IS
INFLUENCED BY CONDUCTIVE PROPERTY OF MATERIAL
CONDUCTANCE (g) unitssiemens,S measure of
materials ease in allowing movement of charged
particles RESISTANCE (R) unitsOhms,W measure
of materials difficulty in allowing electrical
conduction
Resistance is the INVERSE of Conductance. I.e.
1 g
1 R
g
R
OR
4VOLTAGE 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
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 Where q amount of
charge units coulombs, Q and t time
units seconds, s
NOTE I gt 0 means net flow of positive charge I
lt 0 means net flow of negative charge
5OHMS LAW
The amount of current flow is directly
proportional to both the voltage differential and
the conductance
I DV x g
I DV / R DV I x R
OR
WATER PRESSURE ANALOGY
SCHEMATIC DIAGRAM
VALVE
I
FLOW RATE
PA
VA
VB
PB
R
Water Pressure is analogous to Voltage
Differential Valve Resistance is analogous to
Electrical Resistance Flow Rate is analogous to
Electrical Current
DV VA  VB IR I DV / R
Flow Rate Water Pressure / RVALVE
6THE IV PLOT OHMS LAW
I DV x g
CONDUCTANCE ( g ) is SLOPE of line in I  V PLOT
In a simple resistive circuit, the relationship
between current and voltage is LINEAR
WEAKER CONDUCTANCE
HIGH CONDUCTANCE
7MULTIPLE RESISTANCES IN SERIES
IN SERIES RESISTANCES SUM TO GIVE OVERALL
RESISTANCE
POSITIVE
NEGATIVE
Two resistances are summed to give the overall
resistance between points a and c Currents
are equal along the series By Ohms Law, the
total voltage differential equals the sum of
the component voltages
RTOTAL (a,c) R1 (a,b) R2 (b,c) ITOTAL
(a,c) I1 (a,b) I2 (b,c) DVTOTAL (a,c)
DV1 (a,b) DV2 (b,c)
8MULTIPLE RESISTANCES IN PARALLEL
R1
I1
POSITIVE
NEGATIVE
ITOTAL
I2
R2
ITOTAL I1 I2 gTOTAL g1
g2 DVTOTAL DV1 DV2 I1 x R1 I2
x R2
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 Ohms Law, larger
current travels thru the path of least
resistance
9CIRCUIT DIAGRAM
ITOTAL
EQUIVALENT REPRESENTATIONS
10BEHAVIOR OF A SIMPLE RESISTIVE CIRCUIT
SWITCH OPEN AT t 0 sec
SWITCH CLOSED AT t 5 sec
I
I
R (10 W )
R (10 W )
10 V
10 V
DV
DV
CIRCUIT PROPERTIES
10
1
I (Amps)
DV (volts)
0
0
0 5
0 5
t (sec)
t (sec)
11CAPACITANCE
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 gt Larger charge
stored A material that has capacitance is
called a capacitor. The schematic symbol for a
capacitor is
C
12BEHAVIOR OF A SIMPLE CAPACITIVE CIRCUIT
SWITCH OPEN AT t 0 sec
SWITCH CLOSED AT t 5 sec
I
I
10 V
10 V
C (10 F )
DV
DV
C (10 F )
CIRCUIT PROPERTIES
10
100
Q (coulombs)
DV (volts)
I (Amps)
0
0
0
0 5
0 5
0 5
t (sec)
t (sec)
t (sec)
13RELATIONSHIP OF CAPACITANCE AND CURRENT
AS DESCRIBED BEFORE
q C x DV
I dq /dt
SINCE
dq/dt I C x dDV/dt
I.e. As current flows into a capacitor, the
voltage across it increases
14CIRCUIT WITH CAPACITANCE RESISTANCE IN SERIES
( REMEMBER After switch closed, DVA DVB
DVTOTAL 10 V )
CIRCUIT PROPERTIES
10
10
2
DVA (volts)
DVB (volts)
I (amps)
0
0
0
5 0 5 10
5 0 5 10
5 0 5 10
t (sec)
t (sec)
t (sec)
15LOGARHYTHMIC DECAY OF CURRENT THROUGH A CIRCUIT
WITH CAPACITANCE RESISTANCE IN SERIES
Equ. A
Equ. B
Combine equations A B and integrate
As capacitor charges, VR and I decay
logarhythmically
16CIRCUIT WITH CAPACITANCE RESISTANCE IN SERIES
CONTROL OF CURRENT FLOW BY SIZE OF R AND C
THE LARGER THE RESISTANCE (R) gt 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) gt THE LONGER IT
TAKES FOR CAPACITOR TO CHARGE
THE
SLOWER THE DECLINE IN CURRENT FLOW
NO EFFECT ON INITIAL CURRENT SIZE
t1/2max (sec) 0.69 x R (W) x C (F)
17CIRCUIT 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 (5 W )
DVA
10 V
C (1 F )
DVB
CIRCUIT PROPERTIES
10
10
RESISTOR VOLTAGE
DVA (volts)
DVB (volts)
0
0
CAPACITOR VOLTAGE
10
10
0 5 10 15 20
0 5 10 15 20
t (sec)
t (sec)
18CIRCUIT WITH CAPACITANCE RESISTANCE IN PARALLEL
SWITCH OPEN BEFORE t 0 sec SWITCH CLOSED AT t
0 sec
ITOT
RA (5 W )
DVA

10 V
IB
IC
RB (5 W )
DVB
C (1 F )
ITOT
2
CURRENT FLOW THROUGH PARALLEL RESISTOR IS
DELAYED BY THE CAPACITOR
I C (amps)
1
0
5 0 5 10
t (sec)
19(No Transcript)
20CIRCUITS WITH TWO BATTERIES IN PARALLEL
SWITCH CLOSED AT t 0 sec
I B (amps)
0
5 0 5 10
t (sec)
IB (VA  VB) / RB
VA VB IBRB
or
VC is the weighted average of the two
batteries, weighted by the conductance through
each battery path
CONCLUSION
21RESISTANCES 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
22MODELLING THE AXON AS RESISTANCES CAPACITANCES
RM
RM
RM
CM
CM
CM
RAXON
RAXON
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.
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).
IM1
IC1
IA1
IA2
23Next lecture ION CHANNELS THE RESTING
MEMBRANE POTENTIAL
REQUIRED READING Kandel text, Chapters 7, pgs
105139