Electronics and projects
Ohm's law
Enter any two of voltage, current, resistance and power and get the other two, with the working.
Class 10 to 12, diploma, makers
Electronics and projects
Series and parallel resistor calculator
Combine any number of resistors in series or in parallel and get the total resistance. Add a supply voltage to see the current and how the voltage or the current shares out between them.
- Made forClass 10 to 12, diploma
- Shows the workingEvery step, ready for your practical file
- Instant answersResults change as you type
Resistors in series or parallel
Add as many resistors as you need (empty rows are skipped). Add a supply voltage to see the current and the share each resistor takes.
Total resistance in series7.9 kΩSeries always adds up to more than the largest resistor.
- Total resistance
- 7.9 kΩ7,900 Ω
- Same resistors in parallel
- 599.8 Ω
- Resistors
- 3
- Total current
- 1.139 mAat 9 V
Working
- R = R1 + R2 + R3
- R = 1 kΩ + 2.2 kΩ + 4.7 kΩ = 7.9 kΩ
- Current from the supply I = V ÷ R = 9 V ÷ 7,900 Ω = 1.139 mA
- Tip: In series the same current flows through every resistor and the voltage divides in proportion to the resistance.
Each resistor at 9 V
| Resistor | Value | Voltage | Current | Power |
|---|---|---|---|---|
| R1 | 1 kΩ | 1.139 V | 1.139 mA | 1.3 mW |
| R2 | 2.2 kΩ | 2.506 V | 1.139 mA | 2.86 mW |
| R3 | 4.7 kΩ | 5.354 V | 1.139 mA | 6.1 mW |
What it works out
Understanding series and parallel resistors
In series, resistors sit one after another: the same current flows through each and their resistances add up. In parallel, they sit side by side across the same two points: each gets the full voltage, the currents add up, and the total resistance is less than the smallest one.
Combining resistors is how you make a value you do not have (two 1 kΩ in parallel make 500 Ω), build a voltage divider for a sensor, and understand why every appliance at home gets the full mains voltage.
Formula and worked example
Working out series and parallel resistors by hand
The calculator uses exactly these formulas. Write them in your notebook and check one answer by hand: it is the surest way to remember them.
The formula
- Series: R = R1 + R2 + R3 + …
- Parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
- Two in parallel: R = (R1 × R2) ÷ (R1 + R2)
- R
- total (equivalent) resistance
- R1, R2 …
- the individual resistors, all in the same unit
- n equal resistors
- series gives n × R, parallel gives R ÷ n
Worked example
100 Ω, 200 Ω and 300 Ω
- Series: 100 + 200 + 300 = 600 Ω.
- Parallel: 1/R = 1/100 + 1/200 + 1/300 = 6/600 + 3/600 + 2/600 = 11/600.
- Take the reciprocal: R = 600 ÷ 11 = 54.5 Ω.
- Check: 54.5 Ω is less than the smallest resistor (100 Ω), as a parallel total must be.
Answer600 Ω in series; 54.5 Ω in parallel
In projects and exams
How students use it
Combine any number of resistors in series or parallel; see the total, the current and each share. Here is where it earns its place in a school year.
Board exam numericals
Check equivalent-resistance answers, including mixed networks solved one group at a time.
Making a missing value
No 500 Ω in the kit? Two 1 kΩ in parallel make it. Two 4.7 kΩ in series make 9.4 kΩ.
Voltage dividers
Light and temperature sensors (LDRs and thermistors) are read through a divider; the series formula gives its current and output.
Wiring at home
Household appliances are in parallel, which is why switching one on does not dim the others.
Check your work
Common mistakes to avoid
These are the slips that cost marks in exams and burn out parts on the bench.
Adding parallel resistors
Parallel resistances never simply add; add their reciprocals and then take the reciprocal of the sum.
Forgetting the last step
In parallel, 1/R = 11/600 is not the answer: R is 600/11.
Mixing Ω and kΩ
Convert every value to the same unit before adding, or choose the unit beside each value here.
Treating a mixed network as one type
Solve the innermost series or parallel group first, replace it with its total, and work outwards.
Questions
Questions about series and parallel resistors
Stuck on a project or a sum? Ask the institute on WhatsApp.
Ask on WhatsAppWhy is the parallel total smaller than the smallest resistor?
Each extra resistor in parallel is another path for current. More paths let more current through at the same voltage, which means less total resistance.
How do I solve a mix of series and parallel?
Find a group that is purely series or purely parallel, replace it with its total, redraw, and repeat until one resistor is left. You can do each step here.
What is the total of identical resistors?
n identical resistors R make n × R in series and R ÷ n in parallel. Three 3 kΩ in parallel make 1 kΩ.
Does the order of resistors in series matter?
Not for the total or the current. It changes only the voltage at the points between them, which matters in a voltage divider.
Free ebooks
Read more about series and parallel resistors
Free PDF ebooks in easy English: download, print and share them.
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