Before You Begin, Your Instructor Will Review the Following

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

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 how charges can be stored and transmitted. Today you will examine a model (called a capacitor) of the cell membrane.

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

Thus, capacitance is defined as a measure of the amount of net charge on either one of the conducting plates per volt.

/ d = spacing between the plates
A = surface area of the plates
V = voltage applied across the plates

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.

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.

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: 10-6 F = 1 µF = 1 UF

picofarad: 10-12 F = 1 pF = 1 µµF = 1 UUF

nanofarad: 10-9 F = 1 nF = 1000µµF = 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.

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)?

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:

Activity Guide

Ó 2010 The Humanized Physics Project

Supported in part by NSF-CCLI Program under grants DUE #00-88712 and #00-88780 Page 4 of 4