| Resistor | Resistance | Voltage Drop | Current | Power |
|---|
Series Resistor Formula
When resistors are connected end-to-end in a single current path, their resistances add directly.
Two Resistors in Series
For two resistors the calculation is simply:
Example
If a circuit contains a 100 Ω resistor and a 220 Ω resistor in series:
The equivalent resistance of the two resistors is therefore 320 Ω.
Current Through Series Resistors
An ideal series circuit has only one current path. Therefore the current is the same through every resistor.
For example, if the total resistance is 1 kΩ and the supply voltage is 10 V:
Unlike a parallel network, there is no current splitting between branches in an ideal series circuit.
Voltage Drop Across Series Resistors
Although the current is the same through every resistor, the voltage drop across each resistor depends on its resistance.
Example: 1 kΩ + 2 kΩ From 12 V
The total resistance is:
The current is:
The voltage drops are therefore:
The two voltage drops add back to the 12 V supply: 4 V + 8 V = 12 V.
Power Dissipation in Series Resistors
Each resistor dissipates power according to its resistance and the common circuit current.
Larger Resistance Means More Power
Because the current is identical through each series resistor, a resistor with twice the resistance dissipates twice the power.
The total circuit power can also be calculated directly from the supply voltage and total resistance:
Worked Series Resistor Examples
Two equal resistors.
Simple voltage-divider pair.
Three resistor network.
Mixed-value series network.
Applications of Series Resistors
Voltage Dividers
Two or more series resistors can create a fraction of an input voltage for measurement, biasing and analog circuits.
Current Limiting
Series resistance can limit current in LEDs and other circuits where a controlled voltage drop is required.
Resistance Matching
Multiple resistors can be combined in series to obtain a resistance value that is not readily available as a single component.
Power Distribution
Several resistors can sometimes distribute voltage and heat dissipation across multiple components.
Series vs. Parallel Resistors
| Property | Series | Parallel |
|---|---|---|
| Total Resistance | R₁ + R₂ + ... | 1/RT = 1/R₁ + 1/R₂ + ... |
| Current | Same through each resistor | Splits between branches |
| Voltage | Divides across resistors | Same across each branch |
| Equivalent Resistance | Greater than every individual resistor | Less than the smallest individual resistor |
Practical Series Resistor Design Notes
- Check resistor tolerance. Real resistor values vary around their nominal resistance.
- Check power rating. Each resistor must be able to dissipate its individual calculated power without exceeding its rating.
- Consider temperature. Resistor resistance can change with temperature depending on the component's temperature coefficient.
- Account for the load. A voltage divider or series resistor network can behave differently when another circuit is connected to it.
- Remember that real components are not ideal. High-frequency circuits can be affected by resistor parasitic capacitance and inductance.
- Do not exceed voltage ratings. Individual resistors also have maximum working-voltage limits, which can matter even when their power rating is sufficient.
Related Electronics Calculators
Series Resistor Calculator FAQ
How do you calculate resistors in series?
For resistors connected in series, the total resistance is the sum of all individual resistances: Rtotal = R1 + R2 + R3 + ... + Rn.
What is the formula for total resistance in series?
The series resistance formula is Rtotal = ΣR, meaning all resistor values are added together.
What happens to current in a series resistor circuit?
The same current flows through every resistor in an ideal series circuit because there is only one current path.
How is voltage divided across series resistors?
The voltage drop across each resistor is proportional to its resistance. For a resistor Ri, Vi = I × Ri. Equivalently, Vi = Vs × Ri / Rtotal.
How do you calculate power for a series resistor?
The power dissipated by each resistor can be calculated using P = I²R. Since the same current flows through all series resistors, a larger resistance dissipates more power.
Can resistors with different values be connected in series?
Yes. Resistors with different values can be connected in series. Their resistance values add together to produce the total resistance.
Does the order of series resistors matter?
For ideal resistors, changing their order does not change total resistance or total circuit current. It does change which physical resistor is associated with a particular position in the circuit.
What is the equivalent resistance of two resistors in series?
For two series resistors, the equivalent resistance is simply Rtotal = R1 + R2.
Can series resistors be used as a voltage divider?
Yes. Two or more series resistors can divide a supply voltage. A two-resistor divider has Vout = Vin × R2 / (R1 + R2), assuming the output load does not significantly affect the divider.