Not given in the exam, recall it.
What it is for
Resistors in parallel is used in Electricity (SPM Physics Form 5). Keep the SI units in every line of working. Electricity
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| R | total resistance | Ω |
| R₁ | first resistance | Ω |
| R₂ | second resistance | Ω |
Rearrangements
R = (R₁R₂) / (R₁ + R₂) (two resistors)1/R₁ = 1/R − 1/R₂
Worked example
Common trap
Understanding resistors in parallel
The equation 1/R = 1/R₁ + 1/R₂ + … gives the total (effective) resistance of resistors connected side by side. Here R is the total resistance, and R₁, R₂ and any others are the individual resistances, all in ohms (Ω).
In parallel each resistor has its own path, so the current splits between them and there are more routes for charge to flow. This lowers the overall resistance: the total is always smaller than the smallest individual resistor.
Every resistor has the same voltage across it.
- For two resistors: R = (R₁R₂) / (R₁ + R₂)
- Or rearrange: 1/R₁ = 1/R − 1/R₂
Add the reciprocals first, then take the reciprocal of the result to get R.
A worked example, step by step
Two resistors R₁ = 12 Ω and R₂ = 4 Ω are connected in parallel. Calculate the total resistance.
Add the reciprocals of the resistances:
- 1/R = 1/R₁ + 1/R₂
- 1/R = 1/12 + 1/4 = 1/12 + 3/12 = 4/12 = 1/3
- R = 3 Ω
The total resistance is 3 Ω. As expected, it is smaller than the smaller resistor (4 Ω).
Remember to take the reciprocal at the very end: stopping at 1/R = 1/3 would give the wrong answer. Using the two-resistor shortcut gives the same result: R = (12 × 4) / (12 + 4) = 48 / 16 = 3 Ω.
Common mistakes and how this is tested
The classic error is forgetting to invert at the end, leaving the answer as 1/R instead of R.
- Adding the resistances directly as if they were in series.
- Using the shortcut R = (R₁R₂)/(R₁ + R₂) for three or more resistors, where it does not apply, use the full reciprocal sum instead.
- Thinking the current is the same in each branch; in parallel the voltage is the same, and the current splits.
This is tested under calculate (find the total, or a missing branch) and explain (why the total resistance is reduced). Check whether the section is series or parallel before combining.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)