Voltage, Current and Resistance

Voltage, Current and Resistance PS Your first exposure to the study of DC electricity has been an experiment in which you applied various voltages to a fixed resistance and measured the I R resulting current. You recorded your results in a table and transferred to Excel to graph. You converted your readings in milliamps to amperes (amps), and plotted V vs I where V is on the vertical axis and I is on the horizontal. V This arrangement goes against the convention which puts the independent variable on the x-axis, but you will see why we do this shortly.

The point of our lab is to see how voltage and current relate to each other and to the resistance in the circuit.

Current is defined as the “rate of flow of charge”. The charge comes from the electrons (or other charged particles, like ions) in the conductor. When a voltage is applied to a conductor, the electrons move from atom to atom, and it is this motion that moves charge along in the conductor. As an electron is dislodged and moves to the next atom it may dislodge a second electron which moves on, or the first electron may move to the next atom. This produces a “drift velocity” for electrons which is many orders of magnitude less than rate at which charge flows which is very nearly the speed of light.

Current, with the symbol I, has units of coulomb’s per second (C/s). One coulomb (C) of charge flowing in 1 second (s) is 1 ampere (A). The ampere is a derived unit. Coulomb is the fundamental unit of charge. The second is the fundamental unit of time.

1 A = 1 C / 1 s

Voltage is the “push” which moves the charge along in a conductor. We think of voltage as a “potential difference” much like the difference in potential energy between two points on a vertical line in a gravitational field. The greater an object is above the ground, the greater its potential energy. The greater a voltage is above “electrical ground” the greater the electrical potential energy, or potential difference.

Voltage, or potential difference, with the symbol V, is measured in volts. One volt is a potential energy (in joules) of 1 J per 1 coulomb of charge, and so voltage has units of joules per coulomb (J/C).

1 V = 1 J / 1 C

We can think of resistance as “friction” which oppose the motion of charge. Resistance is a basic property of matter except for some very special substances called superconductors which appear to have no resistance. Superconductors must be cooled to very low temperatures to become superconducting. A goal in material science is to develop a room temperature superconductor. Metals tend to have low resistances and are called conductors, while nonmetals and most compounds have high resistance and are called insulators. Strong acids and bases and many salts dissolve in water to make ions and produce solutions which are good conductors. Data analysis

Open an Excel spreadsheet and enter a title, the date and your names. Label three columns as I(ma), I(A) and V. Plot your currents in milliamps in the first column. Write a formula to convert from mA to A for the second column, and enter the voltages in the third column. This way you can simply select that last two columns and click the chart wizard icon to begin drawing a graph. Label the x and y axes and let the computer determine the “line of best fit” by doing its linear regression analysis (add a trendline). Be sure to include the formula and R2 values on the graph.

Millard’s Results: Resistor Color Code Start with the band closes to the end of the body of the resistor.

Black 0 Brown 1 Red 2 Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Gray 8 White 9

The first two color bands tell the first two You may have been observant and recorded the color bands on your resistor. If digits. The third band not, your resistor had color bands: RED-RED-RED-GOLD. tells the number of zeros.

Using the color code, predict the resistance of your resistor. Compare that to the A fourth band is the % slope of the line. tolerance. None 20% Using the slope-intercept form of the straight line (y = mx + b), and assuming that silver 10% the y-intercept is close enough to zero to ignore, write an equation for V, I and R. gold 5%

If you wrote: V = R x I, then you have just “discovered” Ohm’s law. Ohm’s law is singly the most important mathematical relationship in electronics.

Ohm’s law is usually written as ….

V V  IR or I  R

Ohm’s Law Problems 1. Write a brief paragraph about the origins of Ohm’s law.

2. The unit for resistance is called the ohm and is given the symbol The Greek letter omega, not a “horseshoe”. Knowing that V = J/C and I = C/s, determine the units to which  is equal.

3. What is the color code for … a. a 100  resistor b. a 3.3 kresistor c. a 5 M resistor

4. Determine the resistance of the following resistors using the color code. Express your answer both in scientific notation (if necessary) for the number of ohms and with either K or M(if necessary). a. BRN-BLK-ORG b. GRN-VIO-YEL c. YEL-YEL-GRN d. RED-BRN-BLK e. VIO-RED-BRN

5. Find the current flowing through a 1000 ohm resistor with a voltage of 13.8 volts applied to it.

6. Find the resistance of a circuit in which a voltage of 25 V produces a current of 0.0045 amperes.

7. Find the voltage across a 25 k resistor through which 80 mA is flowing.

8. Find the current in a lighting strike which covers 6243 feet where the voltage is 260,000 volts and the resistance of the air is 0.003 ohms/foot.

9. Determine the resistance of a piece of wire where the voltage across the wire is 1.35 V at a current of 30.6 amps.

10. A voltage of 9.1V is applied to two electrodes in a solution of copper(II) sulfate. A current of 360 mA is measured. What is the resistance of the solution between the two electrodes?