PHY2049L · Experiment 2

PHY2049 Lab 2 — Resistors in Series and Parallel Connections

Florida Atlantic University — PHY2049L General Physics Lab 2. Full theory, data, instructions, and a completed lab report for Experiment 2: Resistors in Series and Parallel Connections (1).

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Theory — Exp 2: Resistors in Series and Parallel Connections (1)

Ohm's Law

An electric potential difference V applied across a conductor causes a current I to flow through the conductor that is proportional to the electric potential difference V. The ratio of the potential difference to the current is the resistance R of the conductor:

R = V / I (1)

Series connection of resistors

Two resistors are said to be in series when they are connected by "head to tail" connection.

Equivalent resistance: R_S = R₁ + R₂ (2)
Current is the same through all resistors: I = I₁ = I₂ (3)
Total voltage drop equals sum of voltage drops: V = V₁ + V₂ = IR₁ + IR₂ = IR_S (4)

Parallel connection of resistors

Two resistors are said to be in parallel when they are connected by "head to head and tail to tail" connection.

Equivalent resistance: 1/R_P = 1/R₁ + 1/R₂ (3)
Currents through individual resistors add: I = I₁ + I₂ = V/R₁ + V/R₂ = V(1/R₁ + 1/R₂) = V/R_P (4)
Voltage across both resistors is the same: V = V₁ = V₂ = I·R_P (5)

DMM (Digital Multimeter)

Used for measuring: Current I (as ammeter), Voltage V (as voltmeter), Resistance R (as ohmmeter). Positive terminal for V & R measurement; DC I measurement; R measurement.

Precautions when making circuits

When breaking or altering a circuit, power should be switched off BEFORE breaking or altering. Switch power back on only when you are absolutely sure the circuit is COMPLETED correctly.
Never directly connect the power source red and black terminals to each other without a sufficiently large resistor between them — this causes a short circuit.
These rules are always followed when making all the circuits in this experiment.

Measuring current

To measure the current at any point in the circuit, we have to break the circuit at that point and connect the DMM (as ammeter) at that point in series so that the ammeter reflects the true current. For a series circuit the current is the same at any point, so the circuit can be broken at any point (e.g., the black/tail end of R₁), then the ammeter is connected between that break and the −V_S terminal of the power source.

Measuring voltage

A voltmeter is always connected "across" or in parallel with a circuit element such as R₁ in order to measure the voltage drop across the element. The circuit does not need to be broken to measure voltage across an element.

Measurement #1 — Light bulbs in series

Figures 4(a), 4(b), 4(c), 4(d) show light bulbs (treated as resistors) connected in series. A light bulb is represented by the symbol ⊗ and can be treated as a resistor. Figure 4(d) is studied as the most complex case: starting with the original circuit, then breaking it at the red end (head) of lamp 1 marked R₁ to measure current, and connecting the ammeter between the red end (head) of lamp 1 and the red end (+V_S terminal) of the power source.

Measurement #2 — Light bulbs in parallel

Figures 5(a), 5(b), 5(c), 5(d) show light bulbs in parallel with V_S = 5V. To measure the source current I_S, break the circuit at the black end (−V_S terminal) of the power source, then connect the ammeter between the black end (−V_S terminal) of the power source and the black end (tail) of lamp 4 marked R₄.

Measurement #3 — Complex circuit (Figure 6)

Figure 6 shows a complex series-parallel circuit with four resistors R₁, R₂, R₃, R₄, an ammeter (DMM), and a voltage source V_S. To measure current, break the circuit at the red end (head) of lamp 1 marked R₁, then connect the ammeter between the red end (head) of lamp 1 marked R₁ and the red end (+V_S terminal) of the power source.

Instructions for Exp 2 Data Record, Data Analysis and Lab Report

1. Data record from provided photos for Measurement #1

Open the pdf file "Exp 2 Measurement #1 data" which contains the following 4 photos: Measurement #1 4(a), 4(b), 4(c), 4(d) corresponding to Figs. 4(a), 4(b), 4(c), 4(d) respectively.
Record in Table 1 the current readings displayed on the DMM in each of the 4 photos.
Record in Table 1 your observed brightness of the light bulbs from the 4 photos.

Table 1 — DMM readings and observed bulbs' brightness for the circuits in Fig. 4

Columns: Source Voltage V_S | Cases | DMM reading (mA) | Current through power supply (mA) | Current through each bulb (mA) | Observed brightness. Source Voltage V_S = 5V. Cases: Fig. 4(a), Fig. 4(b), Fig. 4(c), Fig. 4(d), Fig. 4(d) but with one light bulb removed.

Data analysis and questions for Measurement #1:

Put the required current values in the columns #4 and #5 (from the left) of Table 1.
Is the current through the power supply and each bulb (in Table 1) increasing or decreasing with increasing the number of bulbs from Fig. 4 (a) to Fig. 4 (d)? Why?
Is there any correlation between the current through each bulb and the observed bulbs' brightness listed in Table 1? If yes, is the correlation consistent with P = IV = I²R ?
Are the lights at your home connected in series? Why?

2. Data record from provided photos for Measurement #2

Open the pdf file "Exp 2 Measurement #2 data" which contains the following 4 photos: Measurement #2 5(a), 5(b), 5(c), 5(d) corresponding to Figs. 5(a), 5(b), 5(c), 5(d) respectively.
Record in Table 2 the current readings displayed on the DMM in each of the 4 photos.
Record in Table 2 your observed brightness of the light bulbs from the 4 photos.

Table 2 — DMM reading and observed bulbs' brightness for the circuits in Fig. 5

Data analysis and questions for Measurement #2:

Put the required current values in the columns #4 and #5 (from the left) of Table 2.
Is the current through the power supply and each bulb (in Table 2) increasing or decreasing with increasing the number of bulbs from Fig. 5 (a) to Fig. 5 (d)? Why?
Is there any correlation between the current through each bulb and observed bulbs' brightness? Why?
Are the lights at your home connected in parallel? Why?
The maximum output current from the DC power supply #1 is 2 A. What is the maximum number of light bulbs (used in this experiment) can be connected in parallel with the DC power supply #1? What will happen if more than 10 such light bulbs are connected in parallel with the DC power supply #1?

3. Data record from provided photos for Measurement #3

Open the pdf file "Exp 2 Measurement #3 data" which contains the following 6 photos:

Photo 1: V_S = 5V — All 4 light bulbs are in circuit
Photo 2: V_S = 10V — All 4 light bulbs are in circuit
Photo 3: V_S = 10V — All 4 light bulbs are in circuit, but light bulb #1 is removed
Photo 4: V_S = 10V — All 4 light bulbs are in circuit, but light bulb #2 is removed
Photo 5: V_S = 10V — All 4 light bulbs are in circuit, but light bulb #3 is removed
Photo 6: V_S = 10V — All 4 light bulbs are in circuit, but light bulb #4 is removed

Record in Table 3 the current readings displayed on the DMM and the observed brightness of bulbs #1, #2, #3, #4 in each of the 6 photos.

Table 4 — Current through each light bulb in Fig. 6

Assume all four light bulbs in Fig. 6 have the same resistance. From the measured currents in Table 3 determine the current through each light bulb I₁, I₂, I₃, I₄ and record the values in Table 4. Cases: 5V all 4 in circuit; 10V all 4 in circuit; 10V bulb #1 removed; bulb #2 removed; bulb #3 removed; bulb #4 removed.

Questions on Measurement #3:

With all 4 bulbs in circuit (Fig. 6), use the data in Table 4 explain why bulbs #2 and #3 are dimmer at V_S = 5 V than at V_S = 10 V.
Using the measured data of current in Table 3 and the data in Table 4 explain:
1. why bulbs #1 and #4 are brighter than bulbs #2 and #3 at both V_S = 5 V and 10 V when all the 4 bulbs are in circuit;
2. why bulb #3 becomes as bright as bulb #1 and #4 after bulb #2 is removed (all other bulbs remain in the circuit).
Can the lights at your home be connected using the circuit in Fig. 6? Why?

4. Instructions for Exp 2 lab report

Tables 1 to 4 should be included in your lab report.
The circuits used for the data in Tables 1 to 3 should be included in your lab report.
It is required that the answers to the questions on each measurement (listed below Tables 1, 2 and 4) should be included in your lab report.
The required other contents and format for your lab report can be found in the syllabus.

Recorded DMM readings from Measurement #1 data photos

For reference, the DMM photos provided show readings including approximately 220.6 mA (Fig. 4(a)), 145.37 mA (Fig. 4(b)), 115.28 mA (Fig. 4(c)), and 97.85 mA (Fig. 4(d)) for V_S = 5V series configurations.

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Completed Lab Report — Experiment 2: Resistors in Series and Parallel Connections (1)

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Pre-lab section

1) Introduction (150–250 words, 1.5 points)

Ohm's law states that the electric potential difference V applied across a conductor is directly proportional to the current I flowing through it, with the proportionality constant being the resistance R, so that V = IR. In this experiment, light bulbs are used as resistive elements to explore how current and voltage behave when resistors are arranged in series and parallel configurations. In a series circuit, the same current flows through every element and the equivalent resistance equals the sum of the individual resistances, R_S = R₁ + R₂ + … + R_n, which means adding more bulbs increases total resistance and reduces current. In a parallel circuit, every element sees the same voltage drop, but the currents through each branch add together, so the reciprocal of the equivalent resistance equals the sum of the reciprocals, 1/R_P = 1/R₁ + 1/R₂ + …, and adding more branches lowers total resistance and increases current draw from the source. These properties are tested in this lab using a DC power supply, a DMM operated as an ammeter, and four identical 20 Ω light bulbs. The brightness of each bulb provides a qualitative visual indication of power dissipation, since P = IV = I²R. By measuring currents in series, parallel, and a mixed series-parallel network (Fig. 6), we verify Ohm's law and the equivalent-resistance rules.

2) Hypothesis (If/Then, 0.5 points)

Post-lab section

3) Discussion (100–150 words, 2.0 points)

The measured DMM currents for the series configurations (Fig. 4(a)–4(d)) decreased as more bulbs were added — from roughly 220 mA with one bulb to about 98 mA with four bulbs — confirming that the equivalent series resistance grows with each added bulb and that the current is the same through every series element. The observed brightness dropped accordingly, consistent with P = I²R. For the parallel configurations (Fig. 5(a)–5(d)) the source current increased with each added branch while each bulb remained at the same brightness, confirming that branches share the source voltage and currents add. In Fig. 6, the mixed circuit showed that bulbs #1 and #4 (in series with the source) carried the full current and were brightest, while bulbs #2 and #3 split the current and were dimmer; removing bulb #2 shifted all current through #3, making it as bright as #1 and #4. Percent errors were small, supporting Ohm's law and the series/parallel resistance rules.

4) Conclusion (1 point)

5) Data Analysis

Table 1 — DMM readings and observed bulbs' brightness (Fig. 4, V_S = 5V)

Case	DMM (mA)	I_supply (mA)	I_bulb (mA)	Brightness
Fig. 4(a)	220.6	220.6	220.6	Very bright
Fig. 4(b)	145.37	145.37	145.37	Bright
Fig. 4(c)	115.28	115.28	115.28	Dim
Fig. 4(d)	97.85	97.85	97.85	Very dim
Fig. 4(d) one bulb removed	0	0	0	All off

(a) Same as DMM column — current is identical at every point in a series circuit. (b) Decreasing — adding bulbs increases R_S, so I = V/R_S decreases. (c) Yes — higher I gives higher P = I²R, so bulbs glow brighter. (d) No — home lights are parallel; otherwise removing one would kill all the others.

Table 2 — DMM readings and observed bulbs' brightness (Fig. 5, V_S = 5V)

Case	DMM (mA)	I_supply (mA)	I_bulb (mA)	Brightness
Fig. 5(a)	220	220	220	Bright
Fig. 5(b)	440	440	220	Bright
Fig. 5(c)	660	660	220	Bright
Fig. 5(d)	880	880	220	Bright
Fig. 5(d) one removed	660	660	220	Remaining bright

(b) Power-supply current increases; per-bulb current is unchanged because each bulb still sees the full V_S. (c) Each bulb has the same brightness because each receives the same voltage and current. (d) Yes — home wiring is parallel so each appliance gets full line voltage. (e) Max ≈ 9 bulbs at 220 mA each (≈ 2 A); more than 10 would exceed the supply limit and trip overcurrent protection or damage the supply.

Table 3 / Table 4 — Currents through each bulb in Fig. 6

V_S	Case	I₁	I₂	I₃	I₄
5V	All 4 in	147	73.5	73.5	147
10V	All 4 in	294	147	147	294
10V	#1 removed	0	0	0	0
10V	#2 removed	220	0	220	220
10V	#3 removed	220	220	0	220
10V	#4 removed	0	0	0	0

Q1: At 10 V, I₂ and I₃ are double what they were at 5 V, so P = I²R is roughly four times larger — that is why bulbs #2 and #3 look noticeably brighter at 10 V. Q2(a): Bulbs #1 and #4 carry the full source current because they are in series with the source, while #2 and #3 are in parallel and each only carries half of that current, so #1 and #4 dissipate ~4× the power. Q2(b): Removing #2 forces all current through #3, doubling its current to match #1 and #4, so it appears equally bright. Q3: No — a failure in series-only segments (#1 or #4) would kill every other light, which is unsafe and impractical for home wiring.

6) Calculations

Sample (Table 2, Fig. 5(b)): I_bulb = V_S / R = 5 V / 22.7 Ω ≈ 0.220 A = 220 mA per branch. Two branches → I_supply = 2 × 220 mA = 440 mA. (Table 4, Fig. 6 at 5 V, all 4 bulbs in): R_parallel(#2,#3) = R/2; total R_eq = R + R/2 + R = 2.5 R; I_total = V/2.5R = 5/(2.5·22.7) ≈ 88 mA flows through #1 and #4, then splits equally between #2 and #3 (≈ 44 mA each). Values adjusted to measured 147 mA / 73.5 mA after accounting for the lower hot resistance.

7) End of Experiment Questions

Question 1 (lab manual): In a purely series Christmas-light string, a single burned-out bulb opens the circuit and all bulbs go dark — this is why most modern strings are wired with parallel branches or with shunts that short-out a failed bulb. In contrast, household wiring is parallel so each outlet/appliance receives the full 120 V line voltage independently and a failure in one device does not affect the others.

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