Lab Report# 5

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An electrical circuit is a path made up of components (e.g. resistors, capacitors, etc), and the wires that connect them, through which an electrical current can flow. In this lab we’ll build several circuits in order to make a voltage divider, test Kirchhoff’s loop and junction rules, and measure the resistivity of copper.

If you haven’t yet studied Kirchhoff’s laws, you should review them for this experiment. Briefly, Kirchhoff’s loop rule states that the total voltage drop over a closed path must equal 0 V, and Kirchhoff’s junction rule states that the current going into a junction, or node, must be equal to the current passing out of the junction.

Learning Goals for this Laboratory:

· Practice constructing more complex circuits

· Learn how to build a voltage divider and become familiar with their use

· Apply Kirchhoff’s laws to a real circuit

· Become familiar with resistivity

Apparatus

Temple University PHysics

Temple University Physics

iOLab Device, iOLab Software, breadboard, wires, resistors, spool of 25 ft of 22 AWG wire, scissors or wire strippers/cutters

7/8/2020 1:41:00 PM

Part I. Voltage Divider

In the first part of the lab we’ll build a very useful circuit called a voltage divider. Quite often a power supply doesn’t provide the voltage desired, so a voltage divider is used to reduce the supply voltage down to the desired level. Voltage dividers are simply a pair of resistors in series with a voltage source. The output voltage is taken between the resistors and is proportional to the input voltage as seen in the circuit diagram in Figure 1. Several variations in for diagramming it are shown.

Vin

Vout

Vin

Vout

Figure 1. Several ways of diagramming a voltage divider. The output voltage is proportional to the input voltage with the constant of proportionality determined by the resistor values.

The voltage divider equation is . This equation shows how easy it is to calculate which resistors one should use to get the desired output voltage.

Question 1. Show that the voltage divider equation is simply a result of applying Ohm’s Law for the voltage across resistor R2 in Figure 1.

Question 2. How can we use our 4.7 and 10 k resistors to get an output voltage of about 1 V from the iOlab’s 3.3 V power supply?

a) Make a voltage divider using any combination of your k ohm resistors (don’t use the 1 resistors for this). Predict the voltage provided at the output of the voltage divider. Build the voltage divider and see if your prediction was correct by measuring the output voltage using the iOlab’s A7 input. Record the results for your lab report, and in the results and discussion section discuss whether the results were as expected. Support your statements using the values you obtained.

Part II. Kirchhoff’s Laws

In this part of the lab we’ll build a circuit with multiple branches to test Kirchhoff’s junction rule and loop rule.

a) Build the circuit in the diagram in Figure 2 below. Don’t forget to connect the bottom most 1 resistor to the ground of the iOlab as indicated in the diagram. Remember that the 1 resistors are for measuring the current through each branch using the high gain G+/G- inputs. There are two 3.3 V outputs on the iOlab, so you can include two voltage sources as shown in the diagram.

Junction at Point B

Figure 2. Circuit for evaluating Kirchhoff's Laws. Loop 3 is the outer loop which includes both voltage sources.

loop 1

loop 2

GND

loop 3

b) Test the junction rule by measuring all the currents into/out of the junction at Point B (see Figure 2). Take care to note the current direction through each of the three branches: conventional current flows from higher to lower voltage, so if you measure a positive voltage, the current is flowing in the direction from the G+ lead to the G- lead. If you measure a negative voltage, the current is flowing from the G- lead towards the G+ lead. Compile your results into a table, making sure to label each branch uniquely and indicate the direction as either toward or away from the junction. Also include in your table the total current into the junction, and the total current out of the junction. In the results and discussion section of your lab report discuss whether your data satisfies Kirchhoff’s junction rule.

c) With the same circuit, test the loop rule for all three loops shown in Figure 2. Do this by using the analog sensor A7 to measure the voltages at each point A, B, C, and D. Make a data table showing all the voltages encountered when going around each of the three loops in the clockwise direction. Be sure to use the correct sign for each voltage, and don’t forget the voltage sources. Review your text if you are unsure how to apply the loop rule. In the results and discussion section of your lab report discuss whether your data satisfies Kirchhoff’s loop rule.

Part III. Resistance and Resistivity

It is well known that some metals are better conductors than others because they allow electrons to move around the metal atoms more freely. Resistivity is the inverse of conductivity, so a good conductor has low resistivity. Here are some resistivity values of common metals:

Material
	Resistivity, ρ
	(Ω·m) at 20 °C
Silver	1.59×10−8
Copper	1.68×10−8
Gold	2.44×10−8
Aluminum	2.65×10−8
Calcium	3.36×10−8
Iron	9.70×10−8
Platinum	1.06×10−7
Tin	1.09×10−7
Lead	2.20×10−7
Stainless steel	6.90×10−7
Mercury	9.80×10−7
Carbon	5×10−4 to 8×10−4

The resistance we are familiar with from Ohm’s Law is a combination of the resistivity of the metal and the shape. Just as a wider drainpipe will allow water to flow more easily, a larger diameter wire will have a lower resistance. Conversely, the wire (or pipe) length increases the resistance. Thus, resistance can be calculated from the material’s resistivity , cross section area , and length using the formula

You may already be familiar with these concepts from studying resistive fluid flow and Poiseuille’s equation for fluid flow.

a) Before you can use the wire coil to measure resistivity, you must first strip the ends so that they can be exposed to and connect to the rest of the circuit. Locate the end of the wire inside the coil by unraveling the coil until it becomes exposed. You can wrap the coil back up once you have pulled the inner end out so that it can be manipulated. Use wire strippers or a sharp knife to strip about 1 cm of the insulating plastic off of both ends of the wire so that we can plug the wire into our iOlab. It should look something like that in Figure 3.

Figure 3. Insulation stripped from both ends of the wire.

b) Construct a circuit with the following elements in series with one another: 10 k resistor, 1 resistor, wire coil. Your circuit should look something like Figure 4. (Be sure to place the resistors in this order, the iOlab reacts oddly when the resistors are reversed).

c) Connect jumper wires to the G+ and G- terminals of the iOLab device. We will be using these wires as a voltage probe. Open the High Gain chart in the iOLab software in order to see the data from these terminals.

Figure 4. Circuit with resistors and long wire.

d) Use the G+/G- wires to touch either end of the 1 resistor to obtain the current through the circuit.

e) Then use the G+/G- wires to find the voltage drop over the wire coil. Use Ohm’s Law to determine the resistance of the coil knowing the voltage across it and current through it.

f) Rearrange the resistance formula for resistivity in terms of resistance , length , and cross section area . Then make use of the fact that the wire coil is 25 feet long and is size 22 AWG where = 0.34 mm2 to calculate the resistivity of copper. Compare this to the accepted value in the table above by calculating percent difference.

R2 R1 R2 R1 R2 1 Ω 1 Ω 10 kΩ 10 kΩ +3.3V A R1 V 1 Ω

+3.3V 4.7 kΩ R2 R1 R2 R1 R2 1 Ω 1 Ω 4.7 kΩ 10 kΩ R1 +3.3V 1 Ω