Our 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.
The 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.
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. Salt water conducts electricity because it has mobile electrons and ionic states via the salt atoms. Salt water provides a large surface area of contact for the conductive element and it connects with the sweat glands so electricity can flow past the skin and into your body, which has low electrical resistance. 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. The dry protein of your skin is an insulator. 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 other students were able to perform this experiment in the discussion forum.
Be extremely careful not to have electrical contact with a voltage source if you have wet or sweaty skin.
Activity 1
Link to the simulation: https://phet.colorado.edu/en/simulations/circuit-construction-kit-dc
Click the Lab icon. Explore the interface!
(a) Use one ideal battery (40 V, 0 Ω internal
resistance), a light bulb (30 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.
What to do if you have problems with the animation speed!
Fill in "Table A" below..
| ΔVBattery | ΔVwire A | ΔVwire B | ΔVBulb | IBulb |
|---|---|---|---|---|
Now use two ideal batteries (30 V, 0 Ω internal resistance), three light bulb (30 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 a way as to they 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. Paste a screenshot of your circuit into your word document.
| ΔVBattery | IBattery | ΔVany Bulb | Iany Bulb |
|---|---|---|---|
(c) Use all the components (two batteries, 3 light bulbs) and connect them in such a way as to they 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. Paste a screenshot of your circuit into your word document.
| ΔVBattery | IBattery | ΔVany Bulb | Iany Bulb |
|---|---|---|---|
Set up the circuit shown on the right with three 30 Ω bulbs and one 30 V battery.
(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 2 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.
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.
Activity 3
Link to the simulation: https://phet.colorado.edu/en/simulations/circuit-construction-kit-ac
Click the Lab icon. Construct a circuit as shown in the diagram below.
Choose R = 50 Ω, C = 0.2 F, V = 9 V.
Use the voltmeter to measure the voltage across the capacitor.
An example is shown below.
With the simulation paused, start by clicking on the capacitor to discharge
it. The initial voltage across the capacitor should be 0 V.
Click the start button on the stopwatch. The stopwatch will start when you
play the simulation. Close switch S1.
You will monitor the voltage across the capacitor as a function of time as the capacitor in the RC circuit is charging. Start the simulation, then pause it at roughly 0.5 V intervals between 1 V and 8.9 V and record the voltage and time in a table in this spreadsheet.
We expect VC = V0(1 - e-t/τ), where V0
= 9 V is the battery voltage. We
can rewrite this as 1 - VC/V0 = e-t/τ,
or ln(1 - VC/V0) = -t/τ.
If we plot ln(1 - VC/V0) versus time the slope will be -1/τ,
where τ is the time constant of the RC circuit.
When the capacitor is fully charged and the voltage across the capacitor is
9V, pause the simulation.
Reset and start the stopwatch.
Open switch S1 and close switch S2.
Monitor the voltage across the capacitor as a function of time as
the capacitor in the
RC circuit is
discharging. Start the simulation, then pause it at roughly 0.5 V intervals
between 8 V and 0.1 V and record the voltage and time in the spreadsheet.
Convert your log into a lab report. See the grading scheme for all lab reports.
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.