4.3.4Electricity and Magnetism
Combined Resistance — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions
5 min read 9 parts Lesson 40 of 65 1 quiz
Lesson summary
4.3.4 Combined Resistance — IGCSE PHYSICS notes: Calculate the combined resistance of resistors in series and in parallel and apply the results to circuit problems.Rtotal = R1 + R2 + R3 + … — the combined resistance is the sum of the individual resistances.What the symbols mean: …
- Adding a resistor
- Equal resistors
- 1 / R = 1 / R1 + 1 / R2
- Two different resistors in parallel
- Making values
- Potential dividers
Part 1 of 7Resistors in series
Rtotal
R1 + R2 + R3 + …
- the combined resistance is the sum of the individual resistances.What the symbols mean: RT = total resistance of resistors in series (Ω) · R1, R2 = the separate resistances (Ω)
Why
- Why the same current passes through each, and the p.d.s add, so I R = I R1 + I R2 + …
Size
- Size the total is greater than the largest individual resistance.
Adding a resistor
- Adding a resistor it always increases the resistance and reduces the current.
Part 2 of 7Resistors in parallel
1Size
- Size the combined resistance is less than the smallest individual resistance.
2Equal resistors
- Equal resistors two equal resistors in parallel give half the resistance of one.
31 / R
1 / R1 + 1 / R2
- the combined resistance of two resistors in parallel (Extended).What the symbols mean: RT = total resistance of resistors in parallel (Ω), always smaller than the smallest one · R1, R2 = the separate resistances (Ω)
- Product over sumR = R1R2 / (R1 + R2).
- For n identical resistors R, Rtotal = R / n.
4Adding a resistor in parallel
- Adding a resistor in parallel it always decreases the total resistance, even a large one.
Part 3 of 7Method for parallel resistors
Method for parallel resistors
Add 1/R1 and 1/R2 to find 1/R.
Use the reciprocal button on the calculator to find R.
Check that the answer is smaller than the smallest resistor.
Part 4 of 7Mixed circuits
1
Identify the groups that are clearly in parallel or in series.
2
Replace each parallel group with its single equivalent resistance.
3
Add the series resistances to get the total.
4
Use I = V / Rtotal to find the supply current.
5
Use the p.d. and current rules to find the values in each part.
Part 5 of 7Reasons for the rules
Reasons for the rules
Series
- Series the electrons squeeze through each resistor in turn, so the opposition adds.
Parallel
- Parallel electrons have several routes, like extra checkout tills, so the overall opposition falls.
Two different resistors in parallel
- Two different resistors in parallel most of the current goes through the smaller one.
Part 6 of 7Applications
Making values
- Making values two 100 Ω resistors in parallel give 50 Ω, and 100 Ω in series with that pair gives 150 Ω.
Potential dividers
- Potential dividers combinations of series resistors are used to divide a supply.
Household circuits
- Household circuits adding an appliance in parallel lowers the total resistance and raises the current from the mains,
- so overloading a socket is a fire risk.
Part 7 of 7More from the specification
More from the specification
Equivalent circuit resistance
- Equivalent circuit resistance calculating series and parallel resistance combinations provides an algebraic means to determine total network current.
Series Resistors Calculation
- When resistors are connected in series, total resistance is the algebraic sum of individual values (R = R₁ + R₂),
- and identical current flows through all components.
Parallel Resistors Calculation
- When resistors are connected in parallel, the reciprocal of total resistance equals the sum of reciprocals,
- (1/R = 1/R₁ + 1/R₂)
- reducing total circuit resistance below any single branch.
Kirchhoff's Current Rule at Junctions
- In parallel circuits, total current from the power source divides among branches at each junction and re-combines before returning to the source.
Electrical Safety and Fuses
- Fuses and earth wires protect appliances by interrupting excessive current to prevent overheating, protecting users and preventing high power dissipation faults.
Current at a junction
- Current at a junction electric current dividing into parallel branches recombines so total current entering any junction remains conserved.
Potential difference across branches
- Potential difference across branches components connected in parallel across a voltage source experience identical potential differences.
Electrical safety fuses
- Electrical safety fuses fuses melt to break electrical circuits when excessive current threatens connected components or appliances.
Components
- Perpendicular parts of a vector that add to give the vector.
Source
- Reservoir at TH providing heat QH
Branch
- Path connecting two junctions.
Junction
- Place where a pipe splits or joins; flow rates add.
Insulation
- Material that reduces thermal energy transfer.
Component
- Part of a vector along one axis.
Circuit diagram
- Drawing of a circuit using standard symbols.
Key terms
| Term | Meaning |
|---|---|
| Combined resistance | Single resistance equivalent to several resistors. |
| Series rule | Rtotal = R1 + R2 + … |
| Parallel rule | 1/R = 1/R1 + 1/R2 + … |
| Reciprocal | The value 1/x; the calculator button is x−1. |
| Equivalent resistance | Resistance that replaces a group of resistors. |
Avoid these mistakes
1
Adding the reciprocals but forgetting to invert at the end — 1/R is not R.
2
Thinking that adding a resistor in parallel increases resistance — it decreases it.
3
Giving a parallel total larger than the smallest resistor.
4
Using the series rule for branches that are in parallel.
Marked practiceQuizzes for this lesson
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