🔌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 + ·sI_1 = I_2 = I_3 = ·sV_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.
Two resistors, 4 Ω and 6 Ω, are connected in series with a 20 V battery. What is the total current?
Three 6 Ω resistors are in series. What single resistor is equivalent?
A 4 Ω and 8 Ω resistor are in series with a 12 V battery. What is the voltage across each resistor?
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?
I = V_1/R_1Two resistors in series with a 24 V battery: R₁ = 2 Ω dissipates 8 W. What is R₂?
P = I² R_1A series circuit has resistors R, 2R, and 3R with a battery voltage V_b. Write an expression for the voltage across the 3R resistor.
Finished reading through this lesson?