Compare the Potential Vs. Current Behavior of a Resistor to That of a Light Bulb

Circuit Labs

Ohm’s Law

The fundamental relationship among the three important electrical quantities current, voltage, and resistance was discovered by Georg Simon Ohm. The relationship and the unit of electrical resistance were both named for him to commemorate this contribution to physics. One statement of Ohm’s law is that the current through a resistor is proportional to the potential difference across the resistor. In this experiment you will test the correctness of this law in several different circuits using two multimeters, one set to measure DCA (ammeter) the other DC V (voltmeter).

These electrical quantities can be difficult to understand, because they cannot be observed directly. To clarify these terms, some people make the comparison between electrical circuits and water flowing in pipes. Here is a chart of the three electrical units we will study in this experiment.

Electrical Quantity / Description / Unit / Water Analogy
Voltage or Potential Difference / A measure of the Energy difference per unit charge between two points in a circuit. / Volt (V) / Water Pressure
Current / A measure of the flow of charge in a circuit. / Ampere (A) / Amount of water flowing
Resistance / A measure of how difficult it is for current to flow in a circuit. / Ohm (W) / A measure of how difficult it is for water to flow through a pipe.

Figure 1

objectives

· Determine the mathematical relationship between current, potential difference, and resistance in a simple circuit.

· Compare the potential vs. current behavior of a resistor to that of a light bulb.

MATERIALS

Vernier Circuit Board
clips to hold wires
light bulb
resistors
2 Multimeters

PRELIMINARY SEtup and QUESTIONS

1. You will have 3 total Volts available in your circuit, calculate the expected current for the circuit if you have:

1 - 10 W resistor
1 - 51 W resistor.
1 - 68 W resistor.

2. Draw a diagram of what a circuit should look like with a battery, 1 resistor, an ammeter and a voltmeter.

PROCEDURE

1. Record the value of the resistor in the data table.

2. With the switch set to External, set your meter to measure the resistance of the resistor and measure the value of the selected resistor.

3. Make a complete circuit using the batteries, circuit board and resistor, and two meters.

Set one meter to the appropriate DCV value level and attach it in parallel to the resistor.
Set one meter to appropriate DCA value level and attach it in series with the resistor.

4. Switch the switch to 3V and Record readings from voltmeter and ammeter.

5. Repeat Steps 1–4 using a different resistor.

6. Replace the resistor in the circuit with a light bulb. Repeat Steps 3 and 4.

DATA TABLE

Current / Voltage
Resistor W
Resistor W
Resistor W
Light bulb

ANALYSIS

As the resistance increased, the current through the resistor should have decreased, dexcribe the relationship you observed.
Make a graph of Current (I) on the y axis vs 1/R on the x axis. You should see a straight line? What is the slope of that line?
Resistance, R, is defined using R = V/I or I = V/R where V is the potential across a resistor, and I is the current. R is measured in ohms (W), where 1W=1V/A. The constant you determined in 2 should be similar to voltage of the system. However, resistors are manufactured such that their actual value is within a tolerance. For most resistors the tolerance is 5% or 10%. Compare your measured value of each resistor to the stated value and determine your measured tolerance. Calculate the range of possible values for each resistor. Does the constant in each equation fit within the appropriate range of values for each resistor?
Do your resistors follow Ohm’s law? Base your answer on your experimental data.
Describe the current and voltage through the light bulb. How did it compare with data found for each resistor?
Assuming your light bulb follows Ohm’s law. Use your graph and calculate its resistance.

Series and Parallel Circuits

Components in an electrical circuit are in series when they are connected one after the other, so that the same current flows through both of them. Components are in parallel when they are in alternate branches of a circuit. Series and parallel circuits function differently. You may have noticed the differences in electrical circuits you use. When using some decorative holiday light circuits, if one lamp is removed, the whole string of lamps goes off. These lamps are in series. When a light bulb is removed in your house, the other lights stay on. Household wiring is normally in parallel.

You can monitor these circuits using a Current Probe and a Voltage Probe, and see how they operate. One goal of this experiment is to study circuits made up of two resistors in series or parallel. You can then use Ohm’s law to determine the equivalent resistance of the two resistors.

objectives

· To study current flow in series and parallel circuits.

· To study voltages in series and parallel circuits.

· Use Ohm’s law to calculate equivalent resistance of series and parallel circuits.

MATERIALS

Vernier Circuit Board
two 10 W resistors
two 51W resistors
two 68 W resistors
Two Multimeters

PRELIMINARY QUESTIONS

Using what you know about electricity, hypothesize about how series resistors would affect current flow. What would you expect the effective resistance of two identical resistors in series to be, compared to the resistance of a single resistor?

2. Using what you know about electricity, hypothesize about how parallel resistors would affect current flow. What would you expect the effective resistance of two identical resistors in parallel to be, compared to the resistance of one alone?

3. Calculate the effective resistance of connecting one of each type of given resistor in series and then parallel

PROCEDURE

Part I Series Circuits

Figure 2

1. Connect the series circuit shown in Figure 2 using the
10 W resistors for resistor 1 and resistor 2. Connect the two meters in the circuit to measure current in the system and voltage across the entire circuit.

2. Reset the circuit to measure the voltage across each individual resistor in the circuit.

3. Repeat Steps 1-2 with a 51 W resistor substituted for resistor 2.

4. Repeat Steps 1-2 with a 51 W resistor used for both resistor 1 and resistor 2.

Figure 3

Part II Parallel circuits

5. Connect the parallel circuit shown in Figure 3 using 51 W resistors for both resistor 1 and resistor2. . Connect the two meters in the circuit to measure current in the system and voltage across the entire circuit.

6. Reset the circuit to measure the voltage and Current across each individual resistor in the circuit.

7. Repeat Steps 14–17 with a 68 W resistor substituted for resistor 2.

8. Repeat Steps 14–17 with a 68 W resistor used for both resistor 1 and resistor 2.

Part III Currents in Series and Parallel circuits

9. For Part III of the experiment, you will use two meters and one of each type of the resistors 10 W, 51 W, and 68 W

Figure 5

10. Connect the parallel circuit as shown in Figure 5 using the 51W resistor and the 68 W resistor in parallel and the 10 W resistor in series.

11. Before you make any measurements, predict the currents and voltage through the three resistors. Will they be the same or different? Note that the two resistors are not identical in this parallel circuit.

12. Connect the meters to measure the current and voltage across the 10W resistor.

13. Reconnect the meters and circuit to measure the current and voltage across the 51W resistor

13. Reconnect the meters and circuit to measure the current and voltage across the 68W resistor.

14. . Reconnect the meters and circuit to measure the current and voltage across the entire circuit

DATA TABLE

Part I Series Circuits

Part I: Series circuits
R1
(W) / R2
(W) / I
(A) / V1
(V) / V2
(V) / Req
(W)
/ VTOT
(V)
1 / 10 / 10
2 / 10 / 50
3 / 50 / 50
Part II: Parallel circuits
R1
(W) / R2
(W) / I
(A) / V1
(V) / V2
(V) / Req
(W)
/ VTOT
(V)
1 / 50 / 50
2 / 50 / 68
3 / 68 / 68
R1
(W) / V / I1
(A)
1 / 10
2 / 51
3 / 68
Circuit

ANALYSIS

Examine the results of Part I. What is the relationship between the three voltage readings: V1, V2, and VTOT?
Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the circuit for each of the three series circuits you tested.
Study the equivalent resistance readings for the series circuits. Can you come up with a rule for the equivalent resistance (Req) of a series circuit with two resistors?
For each of the three series circuits, compare the experimental results with the resistance calculated using your rule. In evaluating your results, consider the tolerance of each resistor by using the minimum and maximum values in your calculations.
Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the circuit for each of the three parallel circuits you tested.
Study the equivalent resistance readings for the parallel circuits. Devise a rule for the equivalent resistance of a parallel circuit of two resistors.
Examine the results of Part II. What do you notice about the relationship between the three voltage readings V1, V2, and VTOT in parallel circuits.
What did you discover about the current flow in a series circuit in Part III?

9. What did you discover about the current flow in a parallel circuit in Part III?

10. If the two measured currents in your parallel circuit were not the same, which resistor had the larger current going through it? Why?

EXTENSIONS

Try this experiment using three resistors in parallel.

Capacitors

The charge q on a capacitor’s plate is proportional to the potential difference V across the capacitor. We express this with

where C is a proportionality constant known as the capacitance. C is measured in the unit of the farad, F, (1farad=1coulomb/volt).

If a capacitor of capacitance C (in farads), initially charged to a potential V0 (volts) is connected across a resistor R (in ohms), a time-dependent current will flow according to Ohm’s law. This situation is shown by the RC (resistor-capacitor) circuit below when the switch is closed.

Figure 1

As the current flows, the charge q is depleted, reducing the potential across the capacitor, which in turn reduces the current. This process creates an exponentially decreasing current, modeled by

The rate of the decrease is determined by the product RC, known as the time constant of the circuit. A large time constant means that the capacitor will discharge slowly.

objectives

· Measure an experimental time constant of a resistor-capacitor circuit.

· Compare the time constant to the value predicted from the component values of the resistance and capacitance.

· Measure the potential across a capacitor as a function of time as it discharges.

· Fit an exponential function to the data. One of the fit parameters corresponds to an experimental time constant.

Materials

Vernier Circuit Board with batteries
4700 mF capacitor
47 and 100 kW resistors
2 D Batteries
Connecting wires
Voltmeter
External Circuit Board

Preliminary questions

1. Consider a candy jar, initially with 1000 candies. You walk past it once each hour. Since you don’t want anyone to notice that you’re taking candy, each time you take just 10% of the candies remaining in the jar. Sketch a graph of the number of candies remaining as a function of time.

2. How would the graph change if instead of removing 10% of the candies, you removed 20%? Sketch your new graph.

Procedure

1. Connect the circuit with the 4700 mF capacitor and the 47 kW resistor in series but do not make a complete circuit with the battery until you are ready to start timing in step 3. Record the values of your resistor and capacitor in your data table, as well as any tolerance values marked on them.

2. Connect the voltmeter across the resistor.

3. Monitor the input to determine the maximum voltage your battery produces.

Charge the capacitor with the switch in the position as illustrated in Figure1.
Watch the reading on the voltmeter screen and note the maximum value reached. You will need this value in a later step.
Record the voltage reading every 5 seconds as the capacitor charges.
Discontinue recording when the voltage reaches 0 or remains constant for 3 consecutive periods.

4. Carefully disconnect the circuit, starting with the capacitor making sure that the capacitor is not in a complete circuit loop.

5. Redesign the circuit with only the resistor and capacitor making a complete circuit. Be ready to record voltages immediately on completing circuit.

6. Measure the voltage as the circuit discharges, record the initial value every 5 seconds until the voltage reaches 0 or stays constant for 3 consecutive periods.

7. Repeat the experiment with the 100 kW resistor in place of the 47 kW resistor. How do you think this change will affect the way the capacitor discharges? Rebuild your circuit using the 100 kW resistor and repeat Steps 1-6.

Analysis

In the data table, calculate the time constant of the circuit used; that is, the product of resistance in ohms and capacitance in farads. (Note that 1W·F = 1 s).

2. Next, fit the exponential function y=Ae–B*x to your data.

Enter time in L1 and Voltage values for the 47 kW resistor in L2 (charging data) and L3 (discharge data) and for the 100 kW resistor in L4 (charging) and L5 (discharge)
Calculate y=Ae–B*x for each list.

3. Print or sketch the graph of potential vs. time.

4 Compare the fit equation to the mathematical model for a capacitor discharge proposed in the introduction,