Studio Session 4

Circuit elements

imageOur bodies separate and store charge as a power source to transmit signals along nerves.  An excess of positive  ions on the outside of the cell membrane results in a potential difference across the membrane.  The inside of the cell is at a negative potential of ~100 mV with respect to the outside.  The membrane acts like a capacitor.

Electrical signals play a role in transmitting information through our bodies.  Sensory information is transmitted via nerves.  Each nerve consists of a bundle of nerve cells or neurons.  A neuron receives stimuli at the input end and produces a signal that is transmitted across the axon to the output end.  The axon membrane can be modeled as a charged capacitor.  When the neuron is stimulated, the voltage across the capacitor rapidly changes and the charge on the plates reverses, only to thereafter quickly return back to its original value.  For this to happen, a current must flow through some effective resistance.  The whole axon can be modeled as a chain of capacitors and resistors connected in series and parallel.  A voltage and current pulse propagates along this chain. 

image

imageThe speed of propagation of the action potential depends on the electrical resistance R within the core of the axon and the capacitance C across the membrane.  A simple electrical circuit, consisting of a resistor in series with a capacitor, has a time constant τ = RC.   The time constant characterizes the time it takes for the capacitor to charge and discharge and therefore limits the maximum speed with which signals can travel through the circuit.

In this laboratory you will experimentally investigate the behavior of simple circuits containing resistors and capacitors.  While you will not model neurons directly, you will become more familiar with how circuits in general behave, and therefore also with how neuron circuits behave.

Equipment needed:

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions.  This log will become your lab report.  Address the points highlighted in blue.  Answer all questions.


The resistance of your body

Fatal electric shock occurs when a sufficiently large electric current flows through the body.  A fraction of such a current flows through the heart and may disrupt the cardiac cycle.  Typical effects are listed in the table below.

Shocking current:     Effect:
<1 mA no observable effect
~1 mA - ~10 mA tingling sensation
~10 mA - ~100 mA muscular paralysis ("can't let go")
~100 mA ventricular fibrillation
~1A - ~10 A thermal damage to tissue

Paradoxically, brief currents of > 1 A may be less dangerous than lower currents.  Instead of putting the heart into ventricular fibrillation, these currents clamp the whole heart muscle at the same time.  When the current is turned off, a normal heart beat may resume on its own accord.  Indeed, currents of about 1 A are used clinically to defibrillate the heart.

Experiment 1

imageUse the digital multimeter to measure the resistance of your body.  Switch the meter on the 20 MΩ scale.  Make sure the leads are plugged into the Ω and COM connectors on the lower right of the meter. 

Note:  This multimeter is only for measuring components not connected to a power source.  Do not connect it to a circuit that has power.
Press the thumb of one of your hands against the black and the thumb of the other hand against the red lead.  

Record the values for each member of your group with dry and with wet thumbs.

The salty fluids within the human body are electrical conductors.  The internal resistance of an arm (from hand to shoulder) is less than 100 Ω.  If there is a voltage across this internal resistance, a current will flow and heat will be generated.  If the current is large or the connection time is long enough, this heat will cause burns and destroy tissue.  Fortunately the resistance of dry skin is high.  Using a typical contact area, the skin acts like an approximately (10 - 100) kΩ resistor in series with the internal resistance of the body.  At voltages below about 50 V the dry skin provides safe current limiting protection. 

Be extremely careful not to have electrical contact with a voltage source if you have wet or sweaty skin.


Measuring capacitance

imageAssume you connect two identical metal plates of area A, separated by a non-conducting material which has a thickness d to a battery and a switch, as shown.
When the switch is open, there is no excess charge on either plate.

Discuss what happens when the switch is then closed. 

Experiment 2

imageConstruct a parallel plate capacitor out of two rectangular pieces of metal foil.  The sheets have small "handles".  Attach the leads of the multimeter to those handles and make sure the leads are plugged into the + and - connectors on the lower left of the meter.  Switch the multimeter to the 20 nF scale.

Note:  The metal foil has sharp edges.  Be careful not to cut yourself.

imageSlip the two foil sheets between the pages of a heavy textbook and separate them by 3 pages of the book.  Make sure the foil sheets do not touch each other and "short out".   The areas of the sheets should overlap and the "handles" should stick out on opposite sides.  Weight the book down with another heavy textbook.

(a)  Measure the capacitance of your "parallel plate capacitor" using your multimeter.  Record your measured value.

(b)  Investigate how the capacitance depends on the separation between the two foil sheets.  Take data for at least five different separation distances (in units of number of pages).  Make sure everything except the separation of the two foils stays the same.  Record your data in a table in your log.  Record the dimensions of the foil and calculate its area.

(c)  Use Excel to produce a plot of capacitance C in units of nF versus d in units of number of pages and versus 1/d.  Paste the graphs into your log.  Is either of these graphs linear?

number of pages:   Capacitance (nF)
3  
6  
9  
12  
15  

(d)  Investigate how the capacitance depends on the area of the conducting plates.  Use a separation distance of 3 pages and change the overlap area of the plates to approximately and 1/4 of the total area.  Just move the foils, do NOT fold them.  Record your data in a table in your log.


Ohm's law?

Ohm discovered that when the voltage (potential difference) across a conductor changes, the current flowing through the conductor changes.  He expressed this as I = V/R or V = IR.  As the voltage increases, so does the current.  For many conductors R is approximately constant.  These materials are called ohmic.  If the voltage across an ohmic resistor is increased, a plot of voltage versus current shows a straight line.  The slope of the line is equal to R.  For non-ohmic materials, R is not constant and a plot of voltage versus current will not show a straight line.

Experiment 3

Use the Pasco RLC board to investigate the relationship between current and voltage in ohmic and non-ohmic materials.


RC circuits

Find out how the voltage across a capacitor varies as it charges and discharges.

Experiment 4


Convert your log into a session report, certify with you signature that you have actively participated, and hand it to your instructor.