Resistors in Series Calculator

Calculate total resistance, current, and individual voltage drops for series circuits using R_total = R₁ + R₂ + ....

⚡ Circuits📐 R = R₁+R₂+...🔌 Series

Enter up to 5 resistor values and supply voltage. Leave unused fields blank.

R₁ (Ω)
R₂ (Ω)
R₃ (Ω)
R₄ (Ω)
R₅ (Ω)
Supply voltage (V)
⚠️ Enter at least one resistance value.

What Is Resistors in Series?

In a series circuit, all components share the same current. Total resistance is simply the sum of all individual resistances: R_total = R₁ + R₂ + R₃ + .... This makes series resistor combinations easy to analyze — adding resistors always increases total resistance.

By Ohm's Law, the current through a series circuit is I = V_supply / R_total. This same current I flows through every resistor in the string. The voltage drop across each resistor is Vᵢ = I × Rᵢ. All voltage drops sum to the supply voltage: V₁ + V₂ + ... = V_supply (Kirchhoff's Voltage Law).

Power dissipated in each resistor: Pᵢ = I² × Rᵢ = Vᵢ × I = Vᵢ²/Rᵢ. Resistors with higher R dissipate more power. Total power: P_total = I² × R_total = V_supply × I. In LED circuits, series resistors limit current and 'drop' the excess voltage between supply and LED forward voltage.

Series resistors have many practical applications: voltage dividers (with two resistors), current limiting (LED resistors), pull-up/pull-down resistors in digital circuits, and attenuation networks in audio equipment. Understanding series resistance is fundamental to all circuit analysis.

Formula Reference Table

Solve ForFormulaNotes
Total resistanceR_total = R₁ + R₂ + ... + RₙOhms; always larger than any single Rᵢ
CurrentI = V_supply / R_totalSame current through all resistors
Voltage drop (each)Vᵢ = I · RᵢProportional to resistance
KVL (Kirchhoff)V₁ + V₂ + ... = V_supplyVoltage drops sum to supply
Power (each)Pᵢ = I² · RᵢWatts
Total powerP = V_supply · I = I² · R_totalEqual to sum of individual powers

3 Worked Examples

Example 1
Three Resistors + Voltage Drops

100 Ω, 220 Ω, 470 Ω in series at 12 V.

  • R_total = 100 + 220 + 470 = 790 Ω
  • I = 12 / 790 = 15.19 mA
  • V₁ = 15.19e-3 × 100 = 1.52 V; V₂ = 15.19e-3 × 220 = 3.34 V; V₃ = 15.19e-3 × 470 = 7.14 V
  • Check: 1.52 + 3.34 + 7.14 = 12.0 V ✓
✓ R_total = 790 Ω; I = 15.2 mA
Example 2
LED Current Limiting Resistor

LED needs 2.0 V, 20 mA. Supply = 5 V.

  • Voltage across resistor = 5 − 2.0 = 3.0 V
  • R = V/I = 3.0 / 0.020 = 150 Ω
  • Use nearest standard: 150 Ω or 180 Ω (slightly reduces current for safety)
✓ LED series resistor = 150 Ω
Example 3
Fault Detection — Open Circuit

Two 1 kΩ resistors at 9 V. One opens (becomes infinite resistance).

  • R_total → ∞; I → 0 mA
  • All 9 V appears across the open resistor; 0 V across good one
  • This is how open-circuit faults manifest in series circuits
✓ Open circuit: I = 0; full voltage across fault

Real-World Applications

💡
LED Circuits
Every LED requires a series resistor to limit current to its rated value (typically 10–30 mA). R = (V_supply − V_LED) / I_LED. Without it, the LED draws unlimited current and burns out instantly.
🔌
Voltage Dividers
Two series resistors divide voltage proportionally. V_out = V_in × R₂/(R₁+R₂). Used in sensor circuits, bias networks, and analog signal conditioning.
🎛️
Pull-Up/Down Resistors
In digital circuits, pull-up resistors (1–100 kΩ) connect GPIO pins to VCC through series resistance, defining the idle logic level while allowing low current when the pin is driven low.
🎵
Audio Attenuation
L-pads and resistive attenuators use series/shunt resistors to reduce audio signal levels without distortion. Impedance matching networks use series resistors to match source to load impedance.
🔬
Wheatstone Bridge
A Wheatstone bridge uses four resistors to measure unknown resistance with high precision. Analyzing it requires understanding series and parallel resistance combinations and voltage divider action.

Common Mistakes to Avoid

⚠️
Adding series resistance to get less

Series resistors always add — total R is always greater than the largest individual value. If your calculation gives a smaller total, recheck.

⚠️
Assuming equal voltage drops

Voltage drops are proportional to resistance: V₁/V₂ = R₁/R₂. Only equal resistors share voltage equally. Larger resistors have larger drops.

⚠️
Current differs through each resistor

WRONG — in series, current is identical everywhere in the loop. I is the same through R₁, R₂, and R₃.

⚠️
Short circuit confusion

If one resistor = 0 Ω (shorted), it's ignored. But if R_total ≈ 0 with high voltage, current becomes dangerously high. Shorts cause fuse/breaker trips.

⚠️
Using kΩ and Ω without converting

Mix of kΩ and Ω: convert all to Ω first. 1 kΩ = 1,000 Ω. Mixing them causes errors by factors of 1,000.

Frequently Asked Questions

Why is series resistance simply additive? ▾
Each resistor in series impedes the same current flow. The total opposition is the sum of each component's opposition. Mathematically: V = I·R₁ + I·R₂ + ... = I(R₁+R₂+...) = I·R_total, so R_total = R₁+R₂+...
What is Kirchhoff's Voltage Law (KVL)? ▾
KVL states that the sum of voltage drops around any closed loop equals zero. In a series circuit: V_supply − V₁ − V₂ − ... = 0, so V₁ + V₂ + ... = V_supply. It is derived from conservation of energy.
How do I choose a current-limiting resistor for an LED? ▾
R = (V_supply − V_forward) / I_desired. For a red LED (V_f ≈ 2.0 V) at 20 mA with 5 V: R = (5−2)/0.020 = 150 Ω. Use the nearest standard resistor value ≥ calculated value to prevent overcurrent.
What happens when one series resistor fails open? ▾
No current can flow in the entire series circuit — an open anywhere breaks the loop. All supply voltage appears across the open point (where R→∞); other resistors see 0 V (since I = 0).
What happens when one series resistor fails short? ▾
The short reduces R_total, increasing current through all remaining resistors. They may overheat and fail. If all resistors short, R_total → 0 and current → V/0 = ∞ — limited only by source impedance and causing blown fuses or fires.
How do series resistors form a voltage divider? ▾
With two resistors R₁, R₂ across V_supply: V_out (across R₂) = V_supply × R₂/(R₁+R₂). The ratio of output to input voltage equals the ratio of R₂ to total resistance. This is one of the most fundamental circuit building blocks.
When are series vs. parallel resistors used? ▾
Series: for voltage division, current limiting, impedance building. Parallel: for current combining, resistance reduction, redundancy. Most real circuits use both in combination — Kirchhoff's Laws handle any mixed network.
What is the resistor color code? ▾
4-band: Band1+Band2 (digits) × Band3 (multiplier) ± Band4 (tolerance). Brown-Black-Red-Gold = 1, 0, ×100, ±5% = 1,000 Ω ±5% = 1 kΩ 5%. 5-band codes add a third digit. Use a resistor color code calculator or multimeter to verify values.

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