ICS 331-L Project 1

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You will only get credit for this lab if the TA checks you off for the lab assignments listed below.

Basic Principles

The purpose of this project is to familiarize yourself with the basic concepts of electricity, specifically including voltage (V), current (I), resistance (R), and power. The first three are related by Ohm's law:

V = IR

For example, if a voltage of 5V is placed across a 1000 Ohm (1 KOhm) resistor, the resulting current is 0.005A (0.005 Amps) or 5mA (five milliAmps). On the other hand, if we measure a current of 10mA flowing through a 2K Ohm resistor, we can deduce that the voltage is 20V.

A physical analogue to these quantities is often made with water pipes. Voltage is analogous to the difference in height between two points connected with a pipe, current to the flow in a pipe, and resistance to the narrowness of the pipe. As the height difference between two ends of a pipe increases (voltage between two ends of a resistor), so does the pressure, causing a greater flow (current). Using a narrower pipe (more resistance) will reduce the flow (current) for a given voltage.

Resistors come in a wide variety of resistances. Most resistors are color-coded to indicate the rated resistance (which may be up to 20% different from the actual resistance). A variety of web resources give the translation, including http://webhome.idirect.com/~jadams/electronics/resistor_codes.htm.

Power is the product of voltage and current:

P = VI = (by Ohm's law) V²/R = I²R

Warnings

Batteries and power supplies are generally designed to provide a constant voltage, up to a maximum current. As the current approaches this maximum, the voltage will begin to drop. This is generally destructive and should be avoided at all costs (or you may have to pay the cost to replace the battery or power supply!). A wire is designed to have very low resistance, and therefore if a voltage is placed across a wire we have a short circuit, drawing as much current as the voltage source is able to supply. Short circuits are also to be avoided at all costs, since they cause the above-mentioned destructive maximum current draw. In such a situation with high current and non-zero voltage, the electrical power consumption becomes very high. This power is converted to heat (some resistances, such as filament lightbulb, convert significant amounts of electrical power to light, but most electrical resistors simply convert electrical power to heat power). This heat can be hazardous by causing burns or fires.

High voltage can also be hazardous, but most of the voltages used in the lab are 5V or less, which is not hazardous. However, even such low voltages can produce sparks, which can cause burns or other problems. It is best to connect everything first with the power turned off, then use a switch to turn on the power to the equipment. Switches are designed to avoid or contain sparks.

Applications

There are many applications of Ohm's law. This project aims to familiarize you with two of them, namely power consumption by electrical heating, and voltage dividers.

Electrical Heating

If you turn on an electrical stove, it gets hot. The elements in the stove have relatively low resistance, and the voltage across them (110V) is relatively high. As a result, a high current flows through the elements, and large amounts of electrical power are converted to heat. This heat leaves the electrical element and heats the pot on the stove.

Lab Assignment:

Using the resistor color chart, determine the colors you would expect to find on a 100-Ohm resistor, and select such a resistor.
Measure and record the resistor's resistance using an ohm-meter. How close is it to the rated resistance?
Connect the 100-Ohm resistor between the power and ground outputs of a 5V power supply.
Before turning on the power, compute the current and power that you expect to see.
Turn on the power. Does the current shown on the power supply match your calculation?
Touch the resistor. Is it getting warm?
Turn off the power, remove the resistor from the power supply, then, while the resistor is still warm, measure and record the resistance. Can you detect any difference?
This resistor is a 1/4W resistor, meaning it might overheat and be damaged if given more than 1/4W. What is the maximum safe voltage that can be applied across the leads of this resistor?

Voltage Divider

If two resistors are connected in series, the same current will flow through both. Since I = V₁ / R₁ and the same current I = V₂ / R₂, we have that V₁ / R₁ = V₂ / R₂, which means that V₁ / V₂ = R₁ / R₂. For a given voltage V = V₁ + V₂ across the series resistors, we see that the voltage has been divided. Since the resistance of two resistors in series is simply the sum of their resistances, so in our case R = R₁ + R₂, a little math will show that V₂ has the value V₂ = V R₂ / (R₁ + R₂) as seen in the following diagram.

Lab Assignment:

Derive the above formula for V₂ (Vdiv). Be sure you understand it well enough that you could reproduce this derivation on an exam, if necessary.

The symbol at the left stands for a battery (or a power supply), with the longer lines (on top in this and most diagrams) marking the positive side. The symbols at the bottom stand for ground, which is defined as the zero-volt level. All grounds in such a diagram are assumed to be connected to all other grounds, though when actually building a circuit you will have to make sure that in fact they are connected by an actual physical wire. Frequently this ground is represented by a triangle with the vertex downwards, whereas the power supply can be represented by a triangle with the vertex upwards (in which case the battery is omitted). The power supply is frequently referred to as Vcc (Voltage -- Continuous Current, what we usually call DC or Direct Current), as in the following figure, representing the same circuit as above:

This kind of voltage divider is most interesting when R₁ or R₂ can be varied. In this case, a change in resistance results in a change of voltage. This change in resistance is not linear -- doubling the resistance does not double the voltage. However:

If the change in resistance is small, and especially if the other resistor is large, then (R₁ + R₂) does not change much, and so the change in voltage is nearly linear. For example if R₂ changes resistance by 0.01% in response to a 1-degree change in temperature (such a resistor is called a thermistor), the voltage change will almost be proportional to temperature change.
Sometimes linearity is unimportant. For example, if we can electronically switch R₂ from a closed circuit (very low resistance) to an open circuit (very high resistance), then the output voltage will be switched from a very low voltage to a very high voltage. For example, if R₂ is a relay that is closed when power is applied, then the voltage is high exactly when no power is applied. This is one way of building a digital inverter, though usually a transistor is used instead of a relay.
Other times, the resister R₁ is simply used to limit the current through the component used in place of R₂. For example, a Light Emitting Diode (LED) will let no current through if the voltage is low, but will allow through exponentially increasing amounts of current -- an LED is a non-linear component (resistors, in contrast, let through current that is proportional to the voltage, and are therefore linear). At a sufficient voltage, the large current implies a large power and the LED burns out. With the voltage divider, the maximum current through the LED is limited to Vcc / R₁, so with a sufficiently large . R₁, the LED will not burn out.

Lab Assignment:

Build the above circuit in the lab using 1000-Ohm resistors for R₁ and R₂, and connect it to the 5V power supply. Verify (using a voltmeter) that the divided voltage is 2.5V.
Build the above circuit in the lab using a 1000-Ohm resistors for R₁ and a 100-Ohm resistor for R₂. Before turning on the power, compute the divided voltage you expect.
Turn on the power, and verify that the voltage matches your computation.
Replace R₂ with a relay. The contacts of the relay should replace the resistor. The coil connections should be connected on one side to a switch connected to power, and on the other side to ground. Verify that the output voltage is low when you energize the relay (and the contacts close), and high otherwise.
Replace R₂ (actually, the relay) with an LED. Note that putting the LED in one way will result in no current and no light, and the other way will result in current and light. Measure and record the voltage across the LED, compute the voltage across R₁, and use that to compute the current through the LED.