HPP Activity 58v2
Storing Charge
Before you begin, your instructor will review the following:



Lab sign-in sheet
Feedback on Lesson 50, including graphical and functional models
Hints for using Excel (Appendix E)
Charge Inside the Body – A Close Look at Cell Membranes
Our bodies store and use charge to transmit signals across nerves and to tell certain cells
what to do and when to do it.
Heart muscle cells are polarized when at rest. This means that the cells have slightly
unequal concentrations of ions across their cell membranes (See picture below). An excess of
positive sodium ions on the outside of the membrane causes the outside of the membrane to
have a positive charge relative to the inside of the membrane. The inside of the cell is at a
potential that is about 90 mV less that the outside of the cell membrane.
Depiction of A Cell Membrane
+
outside the cell
+
+
+
+
+
+
+
+
lipid
bilayer
Layers
of protein
molecules
-
-
-
-
-
-
-
-
inside the cell
This imbalance of charge across a cell membrane is very important. In order to
understand how the human body can transmit signals, one needs to understand the physics of
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 1 of 4
HPP Activity 58v2
how charges can be stored and transmitted. Today you will examine a model (called a
capacitor) of the cell membrane.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 2 of 4
HPP Activity 58v2
Introduction to Capacitors
A capacitor is simply a device made from two conductors of arbitrary shape. These two
conductors are frequently called "plates" and the most common example is a parallel-plate
capacitor. A capacitor is said to be "charged" when its plates carry an equal amount of opposite
charges, +q and -q.
The typical method for transferring equal and opposite charges to a capacitor is to use a
voltage source such as a battery to create a potential difference between the two conductors.
Electrons will then flow off of one conductor (leaving positive charges) and through the
connecting wires on to the other until the potential difference between the two conductors is the
same as that of the voltage source. Note! unless you see a spark, the charges only flow through
the wires, not through the air between the plates. In general, the amount of charge needed to
reach the appropriate potential difference will depend on the size, shape, and location of the
conductors relative to each other. The capacitance of a given capacitor is defined
mathematically as the ratio of the magnitude of the charge, q, on either one of the conductors to
the electric potential difference, V, applied across the two conductors so that
C
q
V
Thus, capacitance is defined as a measure of the amount of net charge on either one of
the conducting plates per volt.
V
-
+
A
d = spacing between the plates
A = surface area of the plates
V = voltage applied across the plates
d
Think about how like charges repel and unlike charges attract as you answer the
following questions:
1.
Consider two identical metal plates of area A, separated by a nonconducting material which
has a thickness d. (This nonconducting material could be air, paper, or protein molecules in
a cell). The plates are connected in a circuit with a battery and a switch, as shown above.
When the switch is open, there is no excess charge on either plate. The switch is then
closed. What will happen to the amount of charge on the metal plate that is attached to the
negative terminal of the battery? What will happen to the amount of charge on the plate
that is connected to the positive terminal of the battery? Explain.
2.
Can excess charges on one plate of a charged parallel plate capacitor interact with excess
charges on the other plate? If so how do they interact?
3.
Is there any limit to the amount of charge that can be put on a plate? Explain.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 3 of 4
HPP Activity 58v2
4.
How would the amount of charge that a pair of parallel plate conductors can hold change
as the area of the plates increases or decreases? Explain your reasoning.
5.
Do you think that the amount of charge a given battery can store on the plates will increase
or decrease as the spacing, d, between the plates of the capacitor increases? Explain.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 4 of 4
HPP Activity 58v2
Application - Quantitative Capacitance Measurements for Parallel Plates
The unit of capacitance is the farad, F, named after Michael Faraday. One farad is equal
to one coulomb/volt. Common capacitance values are often expressed in smaller units. Some
common units and notations are listed below.
microfarad:
picofarad:
nanofarad:
10-6 F =
10-12 F =
10-9 F =
1 µF
1 pF
1 nF
=
=
=
1 UF
1 µµF
1000µµF
=
1 UUF
= 1000 UUF
Note: Sometimes the symbol m is used instead of µ or U on capacitors to represent 10-6, despite
the fact that in other situations m always represents 10-3!
Equipment:
2 sheets of aluminum foil (12 cm x 12 cm); a "fat" textbook; digital capacitance
meter; 2 insulated wires stripped at the ends (~12" long); half-meter stick
You should make a parallel plate capacitor out of two rectangular sheets of aluminum
foil separated by the pages of a textbook. A textbook works well since you can slip the two foil
sheets between any number of pages and weight the book down with something heavy and
non-conducting like another massive textbook. You can then use the capacitance meter to make
the measurements.

You will need to insert short wires into the capacitance slots of the meter to
serve as "probes". Do not let these wires touch each other and “short out”.

When you measure the capacitance of your "parallel plates", be sure the
aluminum foil pieces are arranged carefully so they don't touch each other and
"short out". They should also be situated in the same orientation.

You will need to share the capacitance meter with other lab groups. This
should cause no problems though since the measurements can be completed so
quickly.
Investigation #1:
How does capacitance depend on separation distance?
Devise an experiment to measure 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 and m). Record your data in a table in your logbook. Record the dimensions
of the foil and calculate its area.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 5 of 4
HPP Activity 58v2
Use the graphing guidelines (Appendices A and E) to make a graphical model of your
data by hand or using Excel. You should graph Capacitance vs. spacing distance. Is your data
linear? If not, try graphing C vs. 1/d or C vs. d2.
6.
From your linear graphical model, determine a linear functional model that best describes
the relationship between spacing distance d and capacitance C. How do the results
compare with your prediction (question #5)?
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 6 of 4
HPP Activity 58v2
Investigation #2:
How does capacitance depend on area?
Devise an experiment to measure how the capacitance depends on the area of the
conducting plates. Record the separation distance you use to collect your data and keep this
distance constant. Take data for at least five different values of area. Record your data in a table
in your logbook.
Use the graphing guidelines to make a graphical model of your data. You should graph
Capacitance vs. Area. Is your data linear? If not, try graphing C vs. 1/A or C vs. A2.
7.
From your linear graphical model, determine a linear functional model that best describes
the relationship between surface area of the plates A and capacitance C. How do the results
compare with your prediction (question #4)?
Summary Questions
8.
In words, explain how you think the capacitance of a cell membrane might change if the
cell membrane was made thicker (but the area of the cell remained unchanged).
9.
In words, explain how you think the capacitance of a cell membrane might change if the
cell membrane covered a larger area (but the membrane thickness remained unchanged).
Reference sources:
Workshop Physics ©1990-93 Dept. of Physics & Astronomy, Dickinson College
EKG Sensor © 1996, PASCO Scientific
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 7 of 4