Series-Parallel Circuits (Combination Circuits)

Welcome to Build Circuits With Rich!
In this lesson, we’ll solve a real series-parallel resistor circuit step-by-step using the exact values from the video and verify our answers using KCL and KVL.

What You’ll Learn

How to spot the parallel section inside a larger series circuit
How to calculate the equivalent resistance of two resistors in parallel
How to compute total current, voltage drops, and branch currents
How to verify your work using KCL and KVL

Watch the Video

Circuit Used in This Lesson

Source: Vs = 5 V
Series resistor: R1 = 220 Ω
Parallel resistors: R2 = 470 Ω, R3 = 1000 Ω

Step 1: Find the Parallel Equivalent Resistance (Rp)

R2 and R3 are in parallel, so:

1/Rp = 1/R2 + 1/R3

Or for two resistors only (faster):

Rp = (R2 × R3) / (R2 + R3)

Plug in values:

Rp = (470 × 1000) / (470 + 1000)
Rp = 470000 / 1470
Rp = 319.73 Ω ≈ 320 Ω

✅ Parallel equivalent: Rp ≈ 320 Ω

Step 2: Find Total Resistance (Series + Parallel)

Since R1 is in series with Rp:

Rtotal = R1 + Rp
Rtotal = 220 Ω + 319.73 Ω
Rtotal = 539.73 Ω ≈ 540 Ω

✅ Total resistance: Rtotal ≈ 540 Ω

Step 3: Find Total Current (Itotal)

Use Ohm’s Law:

Itotal = Vs / Rtotal
Itotal = 5 V / 539.73 Ω
Itotal = 0.009264 A
Itotal = 9.26 mA

✅ Total current: Itotal ≈ 9.26 mA

Step 4: Voltage Drop Across the Series Resistor (VR1)

VR1 = Itotal × R1
VR1 = 9.26 mA × 220 Ω
VR1 = 2.04 V (approx)

✅ VR1 ≈ 2.04 V

Step 5: Voltage Across the Parallel Network (Vp)

KVL says the source voltage splits across the series part and the parallel part:

Vs = VR1 + Vp

Vp = Vs − VR1
Vp = 5.00 V − 2.04 V
Vp = 2.96 V

✅ Parallel voltage: Vp ≈ 2.96 V

Important: In parallel, the voltage is the same across both resistors:
VR2 = VR3 = Vp

Step 6: Branch Currents (I2 and I3)

Now find the current in each branch:

I2 = Vp / R2
I2 = 2.96 V / 470 Ω
I2 = 0.006302 A
I2 = 6.30 mA

I3 = Vp / R3
I3 = 2.96 V / 1000 Ω
I3 = 0.002962 A
I3 = 2.96 mA

✅ Branch currents:

I2 ≈ 6.30 mA
I3 ≈ 2.96 mA

KCL Check (Quick Verification)

KCL at the node says total current equals the sum of branch currents:

Itotal = I2 + I3
Itotal = 6.30 mA + 2.96 mA
Itotal = 9.26 mA ✅

Perfect match.

Common Mistakes (Read This)

Forgetting to simplify the parallel network first
Mixing up total current with branch currents
Forgetting that parallel branches share the same voltage
Skipping the KCL/KVL check (it catches mistakes fast!)

Download My Handwritten Notes:

📘 Download Lesson 5 Notes (PDF): Hand Written Notes

Encouraging Bible Verse:

Colossians 3:23
“And whatsoever ye do, do it heartily, as to the Lord, and not unto men;”

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