🔗 Series/Parallel + Voltage Divider

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

        <h3>Parallel Resistors</h3>
        Resistors in parallel: <strong>1/R_total = 1/R1 + 1/R2 + 1/R3 + ...</strong>
        <ul>
          <li>Voltage is the <strong>same</strong> across all resistors</li>
          <li>Current <strong>splits</strong> between branches</li>
          <li>Total resistance is <strong>less</strong> than the smallest resistor</li>
        </ul>

        <h3>Voltage Divider</h3>
        Two resistors in series create a fraction of the input voltage:
        <strong>V_out = V_in × (R2 / (R1 + R2))</strong>

        <div class=

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

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