Lab 3

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 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.

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 (optional)

Do you have a digital multimeter?  Then use it to measure the resistance of your body.  Switch the meter on the 20 MΩ (or closest) scale.  Make sure the leads are plugged into the Ω and COM connectors  of the meter.  Press the thumb of one of your hands against the black and the thumb of the other hand against the red lead.  

Record the measured values 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.

If you do not have a digital multimeter, discuss the outcome of this experiment with students in your lab group who were able to perform this experiment.

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


DC circuits

Activity 1

Link to the simulation: https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc

Click the Lab icon.  Explore the interface!

image(a)  Use one ideal battery (9 V, 0 Ω internal resistance), a light bulb (10 Ω) resistance) and ideal wires (near 0 Ω resistance) to build the circuit shown on the right.  Make sure your light bulb lights up.  Use the voltmeter to measure the potential difference (ΔV) across the battery.  Record only the magnitude of the potential difference (omit +/- signs).  Make a similar potential difference measurement across the bulb and across each length of wire.  With the noncontact ammeter, measure the current through the bulb, IBulb.

Fill in "Table A" below..

ΔVBattery ΔVwire A ΔVwire B ΔVBulb IBulb
         

Now use two ideal batteries (9 V, 0 Ω internal resistance), three light bulb (10 Ω) resistance) and as many ideal wires as needed to build several different circuits.

(b)  Use all the components (two batteries, 3 light bulbs) and connect them in such to produce the most light.  (The largest possible current should flow through the bulbs.  You can connect the batteries and bulbs in series or in parallel as needed.) 

Make measurements and fill in "Table B"  below.

ΔVBattery IBattery ΔVany Bulb Iany Bulb
       

(c)  Use all the components (two batteries, 3 light bulbs) and connect them in such to produce the least amount of light or current, but not zero light or current.  (The smallest possible non-zero current should flow through the bulbs.)

Make measurements and fill "Table C" below.

ΔVBattery IBattery ΔVany Bulb Iany Bulb
       

Set up the circuit shown on the right with three 10 Ω bulbs and one 9 V battery.

 image

(d)  Observe the brightness of the bulbs.

Make measurements and fill in "Table D" below.

ΔVBattery IBattery ΔVBulb 1 IBulb 1 ΔVBulb 2 IBulb 2 ΔVBulb 3 IBulb 3
               

(e)  Change the internal resistance of the battery to 1 Ω.  What happens?

Make measurements and fill in "Table E" below.

ΔVBattery IBattery ΔVBulb 1 IBulb 1 ΔVBulb 2 IBulb 2 ΔVBulb 3 IBulb 3
               

Paste Tables A - E into your log and comment on your measurements.


Ohmic and non-ohmic circuit elements

Activity 2

In a few sentences explain how you can perform and experiment to find out if a circuit element is ohmic or nonohmic.  What measurements do you make and how do you decide, based on the results of your measurements.


RC circuits

Activity 3

imageAssume you have constructed the circuit on the right.  You flip the switch to position (a) and measure the current through the resistor and the voltage across the capacitor as a function of time as the capacitor in the RC circuit is charging.  Your data are plotted figure 1. 
You wait for several minutes, and then you flip the switch to position (b) and again measure the current through the resistor and the voltage across the capacitor as a function of time as the capacitor in the RC circuit is discharging.  These data are plotted figure 2. 
In both tables t = 0 is the time the switch is flipped.  The direction of the current is chosen to be positive if it flows clockwise.

 

image        image
figure 1        figure 2

Convert your log into a lab report.

Name:
E-mail address:

Laboratory 3 Report

Save your Word document (your name_lab3.docx), go to Canvas, Assignments, Lab 3, and submit your document.