650
Ω
0.65
kΩ
0.018462
A
1.8462
V
4.0615
V
6.0923
V
0.2215
W
650
Ω
0.65
kΩ
0.018462
A
1.8462
V
4.0615
V
6.0923
V
0.2215
W
The Resistors in Series Calculator computes the total equivalent resistance of resistors connected end-to-end in a series configuration. When resistors are in series, the same current flows through each one, and the total resistance is simply the sum:
$$R_T = R_1 + R_2 + R_3 + \cdots + R_n$$
This is the simplest resistor combination rule: series resistance always increases the total. The equivalent resistance is always greater than the largest individual resistor in the chain.
In a series circuit, the supply voltage divides among the resistors proportionally to their resistance values. The voltage across each resistor is given by:
$$V_k = I \times R_k = V_{supply} \times \frac{R_k}{R_T}$$
This voltage division principle is the foundation of the voltage divider, one of the most common circuit configurations in electronics. By choosing appropriate resistor ratios, you can scale a voltage to any desired fraction.
Series resistor networks are used in voltage dividers, current limiting, signal attenuation, voltage references, and creating non-standard resistance values from standard components. For example, if you need 470 Ω but only have 220 Ω and 270 Ω resistors, connecting them in series gives 490 Ω — close to the target value.
The total power dissipated in a series circuit equals the sum of power dissipated by each resistor: P_total = P₁ + P₂ + P₃. Since the same current flows through each, power distributes as P_k = I²R_k. The resistor with the highest resistance dissipates the most power and must have an adequate power rating.
This calculator handles up to three resistors (set unused resistors to 0). When a supply voltage is provided, it also computes the series current (I = V/R_T), individual voltage drops, and total power dissipation for complete circuit analysis.
Kirchhoff's Voltage Law (KVL) confirms the results: the sum of voltage drops V₁ + V₂ + V₃ equals the supply voltage, verifying that no energy is gained or lost in the loop.
Enter the resistance values for up to three series resistors (set unused ones to 0). The calculator sums them to find total resistance. If you also provide a supply voltage, it calculates the common series current (I = V/R_T), the voltage drop across each resistor (V_k = I × R_k), and total power dissipation (P = VI).
The total resistance is always the sum of individual values — no resistor can reduce the total. Verify that voltage drops sum to the supply voltage (Kirchhoff's Voltage Law). The highest-value resistor drops the most voltage and dissipates the most power. Ensure each resistor's power rating exceeds its calculated dissipation.
Inputs
Results
Three resistors in series: R_T = 100 + 220 + 330 = 650 Ω. Current I = 12/650 = 18.46 mA. Voltage drops: 1.85 V + 4.06 V + 6.09 V = 12 V (confirms KVL).
Inputs
Results
Need approximately 3.7 kΩ? Combine 1 kΩ + 2.2 kΩ + 470 Ω in series for 3670 Ω. At 5 V, the current is 1.36 mA with total power of 6.8 mW.
In a series circuit, current must pass through every resistor sequentially. Each resistor opposes the current, so the total opposition (resistance) is the sum of all individual resistances. Think of it as making a pipe longer — each section adds more friction to the flow.
Yes. Since R_T = R₁ + R₂ + R₃ + ..., and all resistance values are positive, the total is always greater than or equal to the largest individual resistor. This is the opposite of parallel resistors, where the total is always less than the smallest.
Voltage divides proportionally to resistance. The fraction of total voltage across resistor R_k is V_k/V_total = R_k/R_T. The largest resistor gets the largest voltage drop, and the smallest gets the least. All drops sum to the supply voltage.
Yes, the formula extends to any number: R_T = R₁ + R₂ + ... + Rₙ. For this calculator, set unused resistors to 0. For more than three, calculate partial sums or use the result as one input combined with additional resistors.
If any resistor in a series circuit fails open (infinite resistance), current stops flowing through the entire circuit. This is why series circuits are not used for household wiring — one failed device would disable everything on the circuit.
For each resistor: P_k = I² × R_k, where I is the common series current. Alternatively, P_k = V_k²/R_k using the voltage drop across that resistor. The sum of all individual powers equals the total circuit power.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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