Series Resistor Calculator
Calculate the total equivalent resistance of resistors connected in series. Add any number of resistors and optionally enter a supply voltage to see individual voltage drops across each resistor. See also our Parallel Resistor Calculator and Voltage Divider Calculator.
How to Calculate Series Resistance
When resistors are connected in series, the same current flows through each resistor, but the voltage is divided among them proportionally to their resistance values. The total equivalent resistance is simply the sum of all individual resistances. This is the simplest resistor combination to calculate — just add them up.
Series resistance increases the total resistance of a circuit. Each additional resistor adds to the total opposition to current flow. The voltage across each resistor is proportional to its resistance (voltage divider principle), and the sum of all voltage drops equals the source voltage (Kirchhoff's Voltage Law).
Series Resistance Formula
Total Resistance:
Rt = R1 + R2 + R3 + ... + Rn
Circuit Current:
I = V / Rt
Voltage Drop Across Each Resistor:
Vn = I × Rn = V × (Rn / Rt)
Power Dissipated by Each Resistor:
Pn = I² × Rn = V² × Rn / Rt²
Kirchhoff's Voltage Law:
V = V1 + V2 + V3 + ... + Vn
Example Calculation
Three resistors (100Ω, 200Ω, 300Ω) are connected in series with a 12V supply:
Total Resistance: Rt = 100 + 200 + 300 = 600 Ω
Circuit Current: I = 12V / 600Ω = 0.02A = 20 mA
Voltage Drops:
V1 = 0.02 × 100 = 2.0V
V2 = 0.02 × 200 = 4.0V
V3 = 0.02 × 300 = 6.0V
Check: 2.0 + 4.0 + 6.0 = 12.0V ✓ (equals supply voltage)
Power Dissipation:
P1 = 0.02² × 100 = 40 mW
P2 = 0.02² × 200 = 80 mW
P3 = 0.02² × 300 = 120 mW
Total Power = 240 mW = 12V × 0.02A ✓
Series Resistance Reference Table
| Resistors in Series | Total Resistance (Ω) |
|---|---|
| 100 + 100 | 200 Ω |
| 100 + 200 | 300 Ω |
| 100 + 200 + 300 | 600 Ω |
| 220 + 330 | 550 Ω |
| 470 + 470 | 940 Ω |
| 1k + 1k | 2,000 Ω |
| 1k + 2.2k + 4.7k | 7,900 Ω |
| 4.7k + 10k | 14,700 Ω |
| 10k + 10k + 10k | 30,000 Ω |
| 47k + 100k | 147,000 Ω |
| 100k + 100k | 200,000 Ω |
| 1M + 1M | 2,000,000 Ω |
Frequently Asked Questions
Why does series resistance add up?
In a series circuit, current must flow through every resistor sequentially. Each resistor opposes the current flow, and these oppositions accumulate. Think of it like obstacles on a single-lane road — each one slows traffic further. The total opposition (resistance) is the sum of all individual oppositions.
What is the current in a series circuit?
The current is the same through every component in a series circuit. This is a fundamental property — since there is only one path for current to flow, the same amount of charge passes through each resistor per unit time. The current equals the supply voltage divided by the total series resistance: I = V/Rt.
How is voltage distributed in a series circuit?
Voltage is distributed proportionally to resistance. A resistor with twice the resistance of another will have twice the voltage drop. The fraction of total voltage across any resistor equals its resistance divided by the total resistance: Vn/Vtotal = Rn/Rtotal. This is the voltage divider principle.
What happens if one resistor in a series circuit fails open?
If any resistor in a series circuit fails open (infinite resistance), the entire circuit stops conducting — no current flows through any component. This is a major disadvantage of series circuits. In contrast, if a resistor fails short (zero resistance), the total resistance decreases and current increases, potentially damaging other components.
When should I use series resistors?
Use series resistors to: increase total resistance beyond available single values, create voltage dividers, limit current (current-limiting resistors for LEDs), add resistance for fine-tuning circuits, and create higher-wattage resistors by distributing power across multiple components. Series connection is also used in Christmas lights and some sensor circuits.
How do series and parallel resistors compare?
Series: total resistance increases (Rt = R1+R2), same current through all, voltage divides. Parallel: total resistance decreases (Rt < smallest R), same voltage across all, current divides. Most real circuits use combinations of both (series-parallel networks) to achieve desired resistance values and current/voltage distributions.
Series vs Parallel: Key Differences
Understanding when to use series versus parallel connections is fundamental to circuit design. Series connections are used when you need to increase resistance, divide voltage, or limit current. Parallel connections are used when you need to decrease resistance, maintain voltage across multiple loads, or increase current capacity. Most practical circuits combine both topologies — for example, a string of LEDs with a current-limiting resistor uses series connection, while multiple LED strings are connected in parallel to share a common power supply.
Practical Applications
- LED current limiting: Series resistor limits current through LED (R = (Vsupply - Vled) / Iled)
- Voltage sensing: Series resistor dividers scale high voltages for ADC measurement
- RC timing: Series resistance with capacitance sets time constants in timer circuits
- Pull-up/pull-down: Series resistors set logic levels and prevent floating inputs
- Current limiting: Series resistance protects sensitive components from overcurrent
- Precision values: Combine standard values in series to achieve exact resistance needed