Voltage in Circuits

Theory — Voltage in Series and Parallel Circuits

What is Voltage?

Voltage (V) is the electrical potential difference between two points in a circuit — the "push" that drives current through a resistor. It is measured in Volts (V) using a voltmeter connected in parallel across a component.

Series Circuit

Components are connected end-to-end in a single path. The same current flows through every resistor. The total voltage from the battery is shared (divided) among all resistors in proportion to their resistance.

Series Rules V_total = V₁ + V₂ + V₃ + ...
I = same everywhere
R_total = R₁ + R₂ + R₃ + ...

V_n / V_total = R_n / R_total

Parallel Circuit

Components are connected side-by-side, sharing the same two nodes. Every branch has the same voltage across it — equal to the battery voltage. Current divides among branches inversely proportional to resistance.

Parallel Rules V = same across all branches
I_total = I₁ + I₂ + I₃ + ...
1/R_total = 1/R₁ + 1/R₂ + ...

V_battery = V₁ = V₂ = V₃

Ohm's Law — The Foundation

Ohm's Law V = I × R
I = V / R
R = V / I

Voltage (V) = Current (A) × Resistance (Ω)

Kirchhoff's Voltage Law (KVL)

The sum of all voltage drops around any closed loop in a circuit equals the source voltage. This is the theoretical basis for why voltages add up in series.

Kirchhoff's Voltage Law ΣV_drops = V_source
V_R1 + V_R2 + V_Rh = V_battery

The battery voltage is always fully distributed across the circuit

Instructions — Running the Virtual Experiment

This lab has two circuit types — Parallel (Section A) and Series (Section B). Work through each section in order a, b, c, d as shown on the simulation tabs.

Section A — Parallel Circuit

Measure battery voltage. In the parallel circuit, click the voltmeter probe on the battery. Record V_battery.

Measure voltage across R1. Move the voltmeter to connect across R1. Record the reading. Compare to V_battery.

Measure voltage across R2. Move the voltmeter to connect across R2. Record. Note how it compares to V_battery and V_R1.

Adjust resistor values using the sliders. Observe how changing R1 or R2 affects the voltage readings. In a parallel circuit, voltage across each branch stays equal to battery voltage regardless of resistance.

Section B — Series Circuit

Measure battery voltage. Connect voltmeter across the battery. Record V_battery.

Measure V_R1 and V_R2. Move voltmeter to each resistor. Record both values. Note that V_R1 + V_R2 = V_battery.

Check the ratio. Calculate V_R1/V_R2 and R1/R2. They should be equal — confirming that voltage divides in proportion to resistance.

Add the variable resistor Rh. Enable Rh using the toggle. Move the voltmeter to measure V_R1, V_R2, and V_Rh. Verify that all three sum to V_battery. Change Rh and observe how the voltages redistribute.

Simulation — Circuit Voltage Measurements

Battery

V_battery 9 V

Resistors

R1 (Ω) 300 Ω

R2 (Ω) 500 Ω

Voltmeter Location

V Battery

—

Volts

V across R1

—

Volts

V across R2

—

Volts

I through R1

—

I through R2

—

I total

—

Battery

V_battery 9 V

Fixed Resistors

R1 (Ω) 300 Ω

R2 (Ω) 500 Ω

Variable Resistor Rh

Enable Rh

Rh (Ω) 200 Ω

V Battery

—

Volts

V across R1

—

Volts

V across R2

—

Volts

V across Rh

—

Volts

Current (I)

—

R_total

—

Data Table

Measurement	Circuit	V_Rh (V)
Step a-c	Parallel	N/A
Steps a-c	Series	N/A
Step d (with Rh)	Series+Rh

Team Questions

Question 1. When the voltmeter was connected directly across one resistor in a parallel circuit, how did the reading compare to the battery voltage? Explain based on electrical theory.

a. It was less than battery voltage b. It was equal to battery voltage c. It was greater than battery voltage

Question 2. What would the voltmeter read if connected directly across the second resistor in a parallel circuit (where both resistors are connected to the same battery)?

a. A different voltage than R1 b. The same voltage as R1 — equal to battery voltage c. Zero volts

Question 3. In a series circuit, what relationship exists between the voltage across each resistor and its resistance value?

a. Larger resistance → smaller voltage across it b. Larger resistance → larger voltage across it c. Resistance has no effect on voltage

Question 4. In a series circuit, what is the relationship between the individual voltages across each resistor and the total battery voltage?

a. Each voltage equals the battery voltage b. The voltages multiply to give battery voltage c. The individual voltages sum to equal the battery voltage

Question 5. When the variable resistor Rh was added to the series circuit, what happened to V_R1 and V_R2 compared to before Rh was added? What principle is being demonstrated?

a. V_R1 and V_R2 stayed the same — Rh only affects its own voltage b. V_R1 and V_R2 both decreased — Kirchhoff's Voltage Law redistributes voltage c. V_R1 and V_R2 both increased

Example Lab Report

Physics SC-172 | Section: [Your Section] | Date: [Date]

Lab Members: [Names of all members present]

Purpose

To measure voltage in series and parallel circuits and determine the relationships between individual voltages, total battery voltage, and component resistance values.

Theory

Ohm's Law states V = IR. In a parallel circuit, all branches share the same voltage equal to the battery voltage. In a series circuit, voltage divides among components in proportion to resistance, and the sum of all voltage drops equals the source voltage (Kirchhoff's Voltage Law).

Data Table

Step	Circuit	R1	R2	V_battery	V_R1	V_R2	V_Rh
a–c	Parallel	300 Ω	500 Ω	9.00 V	9.00 V	9.00 V	—
a–c	Series	300 Ω	500 Ω	9.00 V	3.38 V	5.63 V	—
d	Series+Rh	300 Ω	500 Ω	9.00 V	2.70 V	4.50 V	1.80 V

Sample Calculations — Series Circuit (R1=300Ω, R2=500Ω, V=9V)

Total resistance: R_total = 300 + 500 = 800 Ω

Current: I = V/R = 9.00/800 = 0.01125 A = 11.25 mA

V_R1: V = IR = 0.01125 × 300 = 3.375 V ≈ 3.38 V

V_R2: V = IR = 0.01125 × 500 = 5.625 V ≈ 5.63 V

KVL check: 3.38 + 5.63 = 9.01 V ≈ 9.00 V ✓

Voltage ratio: V_R1/V_R2 = 3.38/5.63 = 0.600 R1/R2 = 300/500 = 0.600 ✓ (ratios equal)

Discussion

Q1 — Parallel voltage: The voltmeter read exactly 9.00 V across R1 — identical to battery voltage. In a parallel circuit, all branches connect directly between the same two nodes as the battery. Therefore every branch must have the same potential difference as the source.

Q3 — Series voltage and resistance: V_R1/V_R2 = 3.38/5.63 = 0.600 and R1/R2 = 300/500 = 0.600. The ratios are equal, confirming that in a series circuit, voltage across each resistor is proportional to its resistance: V_n = V_total × (R_n / R_total).

Q5 — Adding Rh: When Rh (200Ω) was added, V_R1 dropped from 3.38 V to 2.70 V and V_R2 dropped from 5.63 V to 4.50 V. This demonstrates Kirchhoff's Voltage Law — the total voltage is still 9.00 V, but it is now shared among three resistors instead of two. Adding resistance reduces current, which reduces the voltage across each original resistor.

Conclusion

The experiment confirmed the fundamental rules of series and parallel circuits. In parallel: all branch voltages equal the source voltage. In series: voltages divide proportionally to resistance and sum to the source voltage. Kirchhoff's Voltage Law was verified experimentally in all configurations.

Practice Questions

Question 1

A 12 V battery is connected to two resistors in series: R1 = 200 Ω and R2 = 400 Ω. Find (a) the total resistance, (b) the current, (c) the voltage across each resistor, and (d) verify using KVL.

Hint: R_total = R1+R2. I = V/R_total. V_n = I×R_n. Check V1+V2 = 12V.

Question 2

Three resistors (150 Ω, 300 Ω, 450 Ω) are connected in parallel across a 6 V battery. Find the voltage across each resistor and the total current drawn from the battery.

Hint: In parallel, V is the same across all. I_n = V/R_n. I_total = I1+I2+I3.

Question 3

A series circuit has a 9 V battery and three resistors. V_R1 = 2.0 V and V_R2 = 3.5 V. What is V_R3? If R1 = 100 Ω, find R2 and R3.

Hint: Use KVL to find V_R3. Then use the ratio V_n/V_total = R_n/R_total to find R2 and R3.

Question 4

In a series circuit with V_battery = 15 V, R1 = 300 Ω, R2 = 500 Ω, a variable resistor Rh is set to 200 Ω. Calculate V_R1, V_R2, and V_Rh. If Rh is doubled to 400 Ω, recalculate all three voltages. What principle does this demonstrate?

Hint: Calculate I = V/(R1+R2+Rh) for each case. Then V_n = I×R_n.

Question 5 — Challenge

A circuit has R1 = 200 Ω in series with a parallel combination of R2 = 400 Ω and R3 = 400 Ω. The battery is 12 V. Find (a) the equivalent resistance of R2 and R3 in parallel, (b) total circuit resistance, (c) total current, (d) voltage across R1, and (e) voltage across R2.

Hint: Find R_parallel = R2×R3/(R2+R3). Then this is in series with R1. The voltage across the parallel combination equals I×R_parallel.