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.

Introduction

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 burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns out in your house, the other lights stay on. Household wiring is normally in parallel.

You can monitor these circuits using a Current and Voltage meters to 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.

Ohm's law relates quantities of voltage and current by resistance:  V(volts) = I(amps)×R(ohms)
where voltage is the potential difference (electric pressure) between two locations and current is the amount of charge flowing between those two locations. Resistance relates current and voltage, thought of as the resistance to flow of electricity.

Resistor Color Codes

Resistors are often labeled with four color bands to indicate their resistance. The bands are read in order, starting at the end of the resistor with a color band nearest it. The first two bands are read as a two digit number. The third band is read as a power of 10 multiplier of that number.

resistance value in ohms = (a two digit number from the first 2 bands) × 10^{(third band digit)}

The fourth band is an indicator of the tolerance of the resistor. The tolerance is stated as a percent of the labeled value, which is the most that the actual resistance can differ from the labeled value.

For example a resistor with the color bands  red/orange/green/gold  would be   23×10⁵W ± 5%

Preliminary Experimental Work

1. Determine the resistance of four different resistors on your desk from their color codes (notice there are two the same of each resistance type). In your notes refer to them as resistors A, B, C, D with A being the lowest resistance and D the highest. The rest of this lab's experiments will refer to them with these letters.

2. The two types of meters on your desk will be used to measure the voltage and current within a circuit. Notice the scale used on the meters is determined by terminal you input the wire. The value on the terminal indicates the maximum on the meter scale.

• The voltmeter (V) measures the potential difference between two points of a circuit. Potential difference (voltage) is measured by connecting the voltmeter across (in parallel) components of the circuit.

• The ammeter (A) measures the current that flows through a wire. Current is measured by breaking the circuit and connecting the ammeter in line (in series) with the circuit.

Notice also the meters have a polarity (positive and negative inputs). The current flow from a battery is directional as indicated by the polarity on a battery. Often the positive side is denoted by red and negative by black.

3. Measure the potential (voltage) of one, two and three batteries connected in series.

4. The animated pictures here illustrate the differences between series an parallel circuit showing current flow as red dots.

• In the series circuit notice the current (the number of red dots) is the same in any part of the circuit.
• For the parallel circuit the current divides between the two parts.

Series Circuits    

1. Prepare a section in your notes for series circuits. Setup in your notes a data table for series circuits. Draw the circuit in your notes. 2. Connect the series circuit shown using the A resistors for both R1 and R2. Then record the following measurements into the data table.

Measure the current in the circuit. Do this by selecting one point in the circuit and break the circuit there. Place the current meter into where you broke the circuit. Press on the switch to complete the circuit and measure the current. Measure the total voltage (Vtot) across R1 and R2. Do this by connecting the voltmeter across both R1 and R2. Press on the switch to complete the circuit and read this voltage. Measure the voltage (V1) across R1. Connect the leads of the Voltage meter across resistor R1 and measure the potential by completing the circuit with the switch. Measure the voltage (V2) across R2. Connect the leads of the Voltage meter across resistor R2. Press on the switch to complete the circuit and read this potential. 3. Repeat the steps with an A resistor for R1 and a B resistor for R2. 4. Repeat the steps using the B resistors for both R1 and R2.

Parallel Circuits  

1. Prepare a section in your notes for parallel circuits. Setup in your notes a data table for parallel circuits. Draw the circuit in your notes. 2. Connect the parallel circuit shown using the C resistors for both R1 and R2. Then record the following measurements into the data table.

Measure the total current (I) in the circuit. Do this by selecting one point in the circuit outside of the two parallel resistors and break the circuit there. Place the current meter into where you broke the circuit. Press on the switch to complete the circuit and measure the current. Measure the total voltage (Vtot) across R1 and R2. Do this by connecting the voltmeter across the R1 and R2 resistors. Press on the switch to complete the circuit and read this voltage. Measure the voltage (V1) across R1. Connect the leads of the Voltage meter across resistor R1 and measure the potential by completing the circuit with the switch. Measure the voltage (V2) across R2. Connect the leads of the Voltage meter across resistor R2. Press on the switch to complete the circuit and read this potential. 6. Repeat the steps with a C resistor for both R1 and a D resistor substituted for R2. 7. Repeat the steps using the D resistors used for both R1 and R2.

Light bulb

Setup a circuit with a light bulb, single battery and a switch all in series. Measure the current in the circuit and voltage across the light bulb. Repeat the steps with two batteries. Repeat the steps with three batteries.

Analysis

Series circuits

1. Examine the results of Series experiment. What is the relationship between the three voltage readings: V₁  V₂  and V_TOT?

2. 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.

3. 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?

4. 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.

Parallel circuits

5. 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.

6. Study the equivalent resistance readings for the parallel circuits. Devise a rule for the equivalent resistance of a parallel circuit of two resistors.

Currents in series & parallel circuits

7. Examine the results of the Currents experiment. What do you notice about the relationship between the three voltage readings V₁  V₂  and V_TOT in parallel circuits.

8. What did you discover about the current flow in a series circuit in the Currents experiment?

9. What did you discover about the current flow in a parallel circuit in the Currents experiment?

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

Light bulb

11. Determine the resistance of the light bulb at the three voltages.