Kirchhoff s Rules. Survey available this week. $ closed loop. Quiz on a simple DC circuit. Quiz on a simple DC circuit

Size: px

Start display at page:

Download "Kirchhoff s Rules. Survey available this week. $ closed loop. Quiz on a simple DC circuit. Quiz on a simple DC circuit"

Christal Pearson
5 years ago
Views:

RC Circuits. Start Magnetic Fields Announcement on MTE 1 This Lecture: RC circuits Membrane electrical currents Magnetic Fields and Magnets Wednesday Oct.

1 RC Circuits. Start Magnetic Fields Announcement on MTE 1 This Lecture: RC circuits Membrane electrical currents Magnetic Fields and Magnets Wednesday Oct. 4, slightly later start time:5:45 pm - 7:15 pm From previous lecture: Resistors and capacitors in series and parallel and examples of DC circuits EMF Kirchhoff s rules Alternate date: Thursday Oct. 5 4:30 pm - 6 pm Survey available this week Kirchhoff s Rules I 1 = I 2 + I 3 Helps us begin to understand how best to conduct the course Helps you get 5 points toward your HW grade Surveys conducted by independent researcher (Shusake Horibe, Physics grad student) through college funding Should have received w/instructions Contact Mr. Horibe (horibe@physics.wisc.edu) if you have problems. Junction Rule: Σ I in = Σ I out Loop Rule: A statement of Conservation of Charge $ closed loop $ " k = #V i closed loop A statement of Conservation of Energy - Quiz on a simple DC circuit Quiz on a simple DC circuit R 1 = R = 2 kω Which is the correct equivalent circuit? R 1 =R =2 kω R 1 =R=2 kω R 2 =R R 3 =R R 2 =R R 3 =R R eq =R/2 R eq =3/2 R = 3 kω R eq =3R = 6 kω R eq = R eq + R 1 = 3/2R=3 kω R eq = 3 kω 1 R eq = 1 R + 1 R = 2 R " R eq = R 2 1

2 Identical Light Bulbs in parallel and series RC Circuits Light Bulbs in series: which is more luminous?

and have the same luminosity " = R dq dt + q C The current becomes zero when the max charge is reached because the potential difference across the capacitor matches

increases from zero to Cε(1-e -1 ) = 63.2% of its maximum Cε In 1τ the current decreases from I 0 =ε/r to ε/r e -1 = 36.

dt = " Q RC e"t / RC The charge decreases exponentially In 1τ = RC, the charge decreases from Q to 36.

8% I 0 q/c = RI I = -dq/dt Membranes as Capacitors (3 lectures ago) We considered membranes as ideal capacitors with C/A = κ C 0 /A = 1 µf/cm 2 (considering a

2 2 Identical Light Bulbs in parallel and series RC Circuits Light Bulbs in series: which is more luminous? and have the same luminosity In which of the 2 cases the bulbs will be more luminous? - parallel - series Light Bulbs in parallel: which is more luminous? and have the same luminosity " = R dq dt + q C The current becomes zero when the max charge is reached because the potential difference across the capacitor matches that supplied by the battery Charging a Capacitor in an RC Circuit Discharging a Capacitor in an RC Circuit q = Cε(1 e -t/rc ) The time constant, τ=rc In 1τ the charge increases from zero to Cε(1-e -1 ) = 63.2% of its maximum Cε In 1τ the current decreases from I 0 =ε/r to ε/r e -1 = 36.8% I 0 The energy stored in the charged capacitor is 1/2 Qε = 1/2 Cε 2 When a charged capacitor is placed in the circuit, it can be discharged q = Qe -t/rc I(t) = " dq dt = " Q RC e"t / RC The charge decreases exponentially In 1τ = RC, the charge decreases from Q to 36.8% Q In 1τ = RC, the current decreases from I 0 = Q/CR = ε/r to 36.8% I 0 q/c = RI I = -dq/dt Membranes as Capacitors (3 lectures ago) We considered membranes as ideal capacitors with C/A = κ C 0 /A = 1 µf/cm 2 (considering a dielectric constant κ = 10) Biological membranes are full of proteins that act as ion channels allowing ionic currents to flow across the membrane You have seen that of the order of 70 ions/channel are needed to depolarize a membrane Ion channels Typical ion channel density (#/µm 2 ): Unmyelinated rabbit vagus nerve 110 Garfish olfactory nerve 35 Lobster walking leg nerve 90 Squid giant axon Rabbit myelinated nerve 23,000 Rat skeletal muscle fibers

C/A = 1 µf/cm 2 Membrane Electrical Model -Q 0 Q 0 The simplest model for a biological membrane is an RC circuit When S is closed (= membrane channel opens) discharge of C RC time constants range

R S Membranes Electrical Model with ion channels Till now we ignored the source of energy (the battery).

neurons) Transmembrane potential Cell membrane with ion channels: C) For a neuron: linear cable model C Nernst potential Let s imagine a membrane permeable only to K + ions.

The transmembrane potential difference ΔV will tend to push K + ions from 2 to 1.

muscle: K+ -98 mv Na+ +67 mv Calculate it from http://www.physiol.usyd.edu.au/daved/teaching/nernst_cal.

equal Variable resistors are used for voltage-gated ion channels, whose resistance changes with voltage.

conductance = 1/ρ A Neurons and axons The human nervous system consists of 10 11 nerve cells = neurons Neurons contain nucleus and axon, a single long thin structure which may be > 1 m long!

3 C/A = 1 µf/cm 2 Membrane Electrical Model -Q 0 Q 0 The simplest model for a biological membrane is an RC circuit When S is closed (= membrane channel opens) discharge of C RC time constants range from 10 µs to 1 s = (R(C/ Hence, specific resistance of membranes: R = ρl/a R A = ρl = Ω cm 2. R S Membranes Electrical Model with ion channels Till now we ignored the source of energy (the battery). Cell membranes behave like non linear or non Ohmic resistors (eg Diode) Basic RC circuit for a membrane superimposed to the bilayer image and a membrane with ion channels (Eg for K + and Na + like in neurons) Transmembrane potential Cell membrane with ion channels: C) For a neuron: linear cable model C Nernst potential Let s imagine a membrane permeable only to K + ions. K + diffuse from compartment 1 to 2, but other ions cannot because the membrane is not permeable to them. 2 becomes electrically positive with respect to compartment 1. The transmembrane potential difference ΔV will tend to push K + ions from 2 to 1. Equilibrium establishes when ΔV is such to move K + ions to the left at the same rate as they tend to diffuse to the right ΔVequilibrium = Nernst potential Typical values in a mammalian skeletal muscle: K+ -98 mv Na+ +67 mv Calculate it from Realistic Electrical Equivalent Circuit of membranes Nernst potential represents equilibrium for a ion species If the transmembrane potential ΔV = ΔV Nernst inward and outward flow of ion A are equal Variable resistors are used for voltage-gated ion channels, whose resistance changes with voltage. If ΔV ΔV Nernst there is a net flow of A one way The K and Na gradients across the membrane are ΔV modeled as voltage sources and the ionic current is I A = G A (ΔV-V Nernst, A ) G A = ion A conductance = 1/ρ A Neurons and axons The human nervous system consists of nerve cells = neurons Neurons contain nucleus and axon, a single long thin structure which may be > 1 m long!! Axons conduct electrical impulses as transmission lines. Typical diameter = 1 µm Length: > 1 m -sciatic nerve: longest axon in human body that runs from the base of the spine to the big toe of each foot. - giraffes have several meter long axons in their neck! In vertebrates, the axons of many neurons are sheathed in myelin The demyelination of axons is what causes the multitude of neurological symptoms found in the disease Multiple Sclerosis. The giant squid axon Functionalities of axon knowledge mostly comes from study of giant squid axon (Nobel prize, 1963, A. Hodgkin and A. Huxley) Dimension: up to 1 mm in diameter; typically around 0.5 mm Controls part of the water jet propulsion system for escaping predators. Between the tentacles of a squid is a siphon through which water can be rapidly expelled by the fast contractions of the body muscles of the animal. This contraction is initiated by action potentials in the giant axon. 3

Action potential nerve pulse = a potential wave that

dependence of action potential in the giant squid

Kung Genetics&Molecule biology Membrane Ion Channels

compass with a magnetic needle (Arabic or Indian

) 800 BC: Greeks discovered magnetite (Fe 3 O 4 )

attract each other N-S Aurora Borealis Magnetic Fields

A vector quantity ( compass needle traces B field

4 Action potential nerve pulse = a potential wave that is the basis of the neural communication V t Time dependence of action potential in the giant squid Honors Lecture on Fri 29 (Ch :05) Prof. C. Kung Genetics&Molecule biology Membrane Ion Channels Everybody welcome! Discover how our nerves and brain work! Magnets 13 th century BC: Chinese already used a compass with a magnetic needle (Arabic or Indian origin?) 800 BC: Greeks discovered magnetite (Fe 3 O 4 ) Magnetic Fields in ordinary life William Gilbert (1600) : Earth is a gigantic magnet! Like poles repel each other N-N or S-S Unlike poles attract each other N-S Aurora Borealis Magnetic Fields Let s Break A Magnet! A vector quantity ( compass needle traces B field lines and points towards N The lines outside the magnet point from N to S Iron filings show the pattern of the electric field lines Electric dipole Magnetic poles are always found in pairs! A monopole has never been observed (but )! - + 4

Electric vs Magnetic Field Lines Field Lines of Bar Magnet Similarities Density gives strength Arrow gives direction Leave +,

S Magnetic field lines don t start or stop.

migrate along the geomagnetic field towards favorable habitats, a behavior known as magnetotaxis.

5 Electric vs Magnetic Field Lines Field Lines of Bar Magnet Similarities Density gives strength Arrow gives direction Leave +, North Enter -, South Differences Start/Stop on electric charge No Magnetic Charge lines are continuous! S Magnetic field lines don t start or stop. N There are no magnetic charges (monopoles) Magnetotacticbacteria Magnetotactic bacteria (MT (Blakemore, 1975) orient and migrate along the geomagnetic field towards favorable habitats, a behavior known as magnetotaxis. MTB are aquatic microorganisms inhabiting freshwater and marine environments. Earth s A Magnet! North magnetic pole is about half way around the Earth (πr E ) from the North geographic pole N geographic pole almost at magnetic S pole S geographic pole almost at magnetic N pole 5

MTE 2: Ch :30-7pm on Mar 26

MTE 2: Ch :30-7pm on Mar 26 MTE 2: Ch 2103 5:30-7pm on Mar 26 Contact me and Prof. Rzchowski after this lecture for Alternate Exams (also by email asap!) 2:30-4pm 6:00-7:30pm on Mar 26 Office hrs change this week Wed morning 1 Contents