Unit 9 · Lesson 3

🔌Series Circuits

Resistors in Series

In a series circuit, components are connected end-to-end in a single loop. There's only one path for current.

Key rules for series circuits: 1. Current is the same through all components: I₁ = I₂ = I₃ = ... 2. Voltage divides: V_total = V₁ + V₂ + V₃ + ... 3. Resistance adds: R_total = R₁ + R₂ + R₃ + ...

The total resistance increases as you add resistors — more obstacles in the path means less current flows overall.

Voltage divider: the voltage across each resistor is proportional to its resistance. Larger R → larger voltage drop.

Series Circuit Simulator

Watch current and voltage in a series circuit. Current is the same everywhere; voltage is shared among resistors.

✏️ Worked Example

Problem: Three resistors (2Ω, 3Ω, 5Ω) are connected in series with a 20V battery. Find the current and voltage across each resistor.

📐 Key Equations

Series circuits

R_series = R_1 + R_2 + R_3 + ·s
I_1 = I_2 = I_3 = ·s
V_total = V_1 + V_2 + ·s

⚠️ Common Mistakes

Misconception: Adding more resistors in series increases the current.

✓ Correct thinking: Adding resistors in series increases total resistance, which DECREASES current (I = V/R_total).

Why: Series resistances add up, so R_total grows. With the same battery voltage, a larger denominator in I = V/R means less current.

Misconception: Each resistor gets the same voltage in a series circuit.

✓ Correct thinking: Voltage is SHARED (divided) among resistors in series. Each resistor gets a voltage proportional to its resistance.

Why: Larger resistors "use up" more of the total voltage: V = IR, and since I is the same, larger R means larger V drop.

Misconception: If one bulb in a series circuit burns out, the others stay on.

✓ Correct thinking: In a series circuit, a break anywhere opens the entire loop. All bulbs go out.

Why: There is only one path for current. Any open break stops current everywhere in the loop.

📝 Practice Problems

Try these problems. Check your answer when ready.

#1

Two resistors, 4 Ω and 6 Ω, are connected in series with a 20 V battery. What is the total current?

easy
#2

Three 6 Ω resistors are in series. What single resistor is equivalent?

easy
#3

A 4 Ω and 8 Ω resistor are in series with a 12 V battery. What is the voltage across each resistor?

medium
#4

In a series circuit, a 3 Ω resistor has 6 V across it. A 5 Ω resistor is also in the circuit. What is the voltage across the 5 Ω resistor?

medium
I = V_1/R_1
#5

Two resistors in series with a 24 V battery: R₁ = 2 Ω dissipates 8 W. What is R₂?

hard
P = I² R_1
#6

A series circuit has resistors R, 2R, and 3R with a battery voltage V_b. Write an expression for the voltage across the 3R resistor.

hard

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