Series Circuits

Lesson 2 of 4: Electrical Circuits

In this lesson:

• Identify series circuits and the one-path rule
• Calculate equivalent resistance:
• Apply Kirchhoff's Voltage Law to find all unknowns

Learning Objectives for This Lesson

By the end, you will be able to:

1. Identify a series circuit and the one-path rule
2. Calculate
3. Find total current using Ohm's Law
4. Find each voltage drop:
5. Verify results with KVL

Why One Bad Bulb Kills All

Old-style Christmas lights: one bulb burns out → all lights go dark

What Makes a Circuit "Series"

• Components connected end-to-end in a single loop
• Only one path for current — through all components
• If any component opens, current stops everywhere
• Current is the same through every component
• Voltage divides:

Series Rules vs. Parallel (Preview)

Quick Check: What Breaks the Circuit?

A series circuit has three bulbs.

If the wire between bulb 1 and bulb 2 is cut:

• What happens to current through bulb 1?
• What happens to current through bulbs 2 and 3?

Think — then advance.

Equivalent Resistance Formula for Series Circuits

• Each resistor adds its resistance — current passes through each in turn
• More resistors in series → larger → less current (for fixed )
• Like passing through multiple toll booths — each one slows you down

Physical Reasoning: Why We Add

Worked Example: Find and Current

, , ;

Step 1:

Step 2: — same through every component.

Worked Example: Effect of Adding a Fourth Resistor

Add a 4th resistor:

→ Adding more series resistors always reduces current.

Quick Check: Find the Equivalent Resistance

Three series resistors: 10 Ω, 20 Ω, 30 Ω with a 12 V source.

What is ? What current flows?

Write the steps before you advance.

Voltage Drops:

• The same current flows through every resistor (series rule)
• Each resistor gets a voltage drop proportional to its resistance
• Larger → larger voltage drop (not more current)

Kirchhoff's Voltage Law Explained Simply

• KVL is a statement of energy conservation
• A charge gaining energy from the battery loses exactly that energy in the resistors
• Use KVL as a verification step — if the drops don't sum to , something went wrong

The Four-Step Series Analysis Procedure

1. Find
2. Find total current:
3. Find each voltage drop:
4. Verify using KVL: ✓

Practice this until it's automatic.

Worked Example: Step 1 — Find

Circuit: , , ,

Worked Example: Find Current and Voltage Drops

Step 2: (same everywhere)

Step 3:

Worked Example: Step 4 — KVL Verification

Proportionality observation:

• → (6 V = 3 × 2 V) ✓
• Voltage divides in the same ratio as resistance

Quick Check: Identify the Voltage Drop

In the worked example (, , , ):

What is the voltage across ?

Guided Practice: Complete the Circuit Analysis

Circuit: , ,

Step 1: (done)

Step 2: Find

Step 3: Find and

Step 4: Verify

Practice: Full Series Circuit Analysis

Solve completely:

, , ,

Find: , , , , . Verify with KVL.

Use the four-step procedure. Show all work.

Practice Answers with KVL Verification

Step 1:

Step 2:

Step 3: , ,

Step 4: ✓

Quick Check: KVL as a Habit

Before submitting any series circuit problem, ask:

Do my voltage drops sum to the source voltage?

If not — there's an error somewhere. Check each step.

Voltage Divider Rule and Application

Useful shortcut: The fraction of source voltage across equals its fraction of total resistance:

Example: In a 60 Ω series circuit, a 20 Ω resistor gets of the source voltage.

Key Takeaways: Series Circuit Essentials

✓ Series: one path, same everywhere,

✓ Four steps: → → each → KVL check

✓ Voltage divides proportionally to resistance

Watch Out: Avoid These Three Errors

Current is not used up — the same flows everywhere in the loop.

The largest gets the largest voltage drop, not more current.

KVL applies to any closed loop, not just simple series circuits.

What Comes Next: Parallel Circuits

sec-19-3: Parallel Circuits

• Multiple independent paths for current
• Voltage is the same across all branches
• Equivalent resistance:
• Kirchhoff's Current Law — the current version of the conservation rule

The rules are exactly inverted from series — compare carefully.