DC Circuits · #3 of 48

Series/Parallel + Voltage Divider

Resistor Combinations

Why it matters

Real circuits combine resistors. Series adds resistance; parallel reduces it. Voltage dividers are everywhere — sensors, level shifting, battery monitoring.

The idea

Series Resistors

Resistors in series: R_total = R1 + R2 + R3 + …

Current is the same through all resistors
Voltage drops across each resistor
Total resistance is the sum

Parallel Resistors

Resistors in parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3 + …

Voltage is the same across all resistors
Current splits between branches
Total resistance is less than the smallest resistor

Voltage Divider

Two resistors in series create a fraction of the input voltage: V_out = V_in × (R2 / (R1 + R2))

flowchart LR
    Vin["V_in"] --> R1["R1"]
    R1 --> Vout["V_out"]
    Vout --> R2["R2"]
    R2 --> GND["GND"]

V_out = V_in × (R2 / (R1 + R2))

Why It Matters

Voltage dividers are used for:

Battery monitoring — scale battery voltage to ADC range
Level shifting — convert 5V signals to 3.3V
Sensor scaling — adjust sensor output to microcontroller range

Demo

Use the calculator to explore:

Series: Enter R1 and R2, see total resistance
Parallel: Enter R1 and R2, see total resistance (always less!)
Voltage Divider: Enter V_in, R1, R2, see V_out

V_in (V) R1 (Ω) R2 (Ω)

Series R1+R2: 37000 Ω
Parallel R1∥R2: 7297 Ω
Divider V_out: 3.07 V
Divider current: 0.114 mA

Key takeaways

Series: R_total = R1 + R2 (resistance adds)
Parallel: 1/R_total = 1/R1 + 1/R2 (resistance reduces)
Voltage divider: V_out = V_in × (R2 / (R1 + R2))
Voltage dividers are used for battery monitoring and level shifting

Going deeper

For parallel resistors, if R1 = R2, then R_total = R1/2. If you have N equal resistors in parallel, R_total = R / N. Voltage dividers have a loading effect — if you connect a load (like an ADC), the effective resistance changes. Use high-impedance inputs or buffer with an op-amp.

Math details

Series resistors:
  R_total = R1 + R2 + R3 + ...

Parallel resistors:
  1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

  For two resistors:
  R_total = (R1 × R2) / (R1 + R2)

Voltage divider:
  V_out = V_in × (R2 / (R1 + R2))

  Current through divider:
  I = V_in / (R1 + R2)

  Power in each resistor:
  P_R1 = I² × R1
  P_R2 = I² × R2

Example: Battery monitoring
  Battery: 4.2V (fully charged LiPo)
  Want: 0-3.3V for ESP32 ADC
  Use: R1 = 10kΩ, R2 = 27kΩ
  V_out = 4.2V × (27k / (10k + 27k)) = 4.2V × 0.73 = 3.07V (safe!)

Implementation

LLM Prompt: Voltage Divider Calculator

Write a Rust function that calculates voltage divider output given V_in, R1, R2.
Include validation: warn if output exceeds 3.3V (ESP32 max) or if current
through divider exceeds 1mA (wasteful for battery-powered devices).

Lab Exercise: Battery Monitor

Design voltage divider: 4.2V LiPo → 0-3.3V for ADC
Calculate R1 and R2 (hint: use R1=10kΩ, R2=27kΩ)
Build circuit on breadboard
Measure V_out with multimeter (should be ~3.07V at 4.2V input)
Verify it scales linearly as battery voltage changes

🔗 Series/Parallel + Voltage Divider