Theme B — The Particulate Nature of Matter
B.5.8 Series and Parallel Circuits — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 49 of 53 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
B.5.8 Series and Parallel Circuits — IB PHYSICS SL notes: Calculate total resistance, current and p.d. in series and parallel circuits.Series — components form a single path, so the same current passes through eachPotential difference — the supply p.d.
- What the symbols mean
- Current division
- Series current
- Series p.d
- Parallel p.d
- Kirchhoff's laws
Part 1 of 8Resistors in series
Series
- Series components form a single path, so the same current passes through each
Potential difference
- Potential difference the supply p.d. is shared between the components, V = V1 + V2 + V3
- The resistor with the largest resistance takes the largest share of the p.d.
Total resistance
- Rtotal = R1 + R2 + R3What the symbols mean: RT = total resistance of resistors in series (Ω) · R1, R2 = the separate resistances (Ω)
- It follows from IRtotal = IR1 + IR2 + IR3.
Size
- Size the total is always larger than the largest individual resistance
- Two equal resistors in series give double the resistance.
- Adding more resistors in series increases the overall resistance.
Part 2 of 8Resistors in parallel
Parallel
- Parallel components are connected between the same two points, so every branch has the same p.d.
Current
- Current the total current splits at a junction and recombines afterwards, I = I1 + I2 + I3
Total resistance
- 1/Rtotal = 1/R1 + 1/R2 + 1/R3What the symbols mean: RT = total resistance of resistors in parallel (Ω), always smaller than the smallest one · R1, R2 = the separate resistances (Ω)
- It follows from using I = V/R in every branch with a common V.
Size
- Size the total is smaller than the smallest branch resistance
- Two equal resistors in parallel give half the resistance.
- Adding more branches provides more paths for charge, so the overall resistance decreases.
Shortcuts
- Shortcuts for two resistors Rtotal = R1R2/(R1 + R2), and N identical resistors R give R/N
Current division
- Current division current divides in inverse proportion to resistance, so the smallest resistance carries the largest current
Part 3 of 8Summary of the rules
| Quantity | Series | Parallel |
|---|---|---|
| Current | Same at every point | Splits: I = I1 + I2 + … |
| Potential difference | Shared: V = V1 + V2 + … | Same across each branch |
| Total resistance | R = R1 + R2 + … | 1/R = 1/R1 + 1/R2 + … |
| Effect of adding a resistor | R increases | R decreases |
Part 4 of 8Why the rules hold
Series current
- Series current conservation of charge means charge cannot accumulate at a component, so the same amount enters as leaves
Series p.d.
- Series p.d. conservation of energy means each coulomb gives up the energy it gained from the source across the components in turn
- The sum of the p.d.s equals the e.m.f.
Parallel p.d.
- Parallel p.d. any route from the positive to the negative terminal has the same energy change per coulomb
Junctions
- Junctions the current into a junction equals the current out of it
Kirchhoff's laws
- Kirchhoff's laws charge is conserved at a junction and energy is conserved around a loop
Part 5 of 8Mixed circuits
1
Replace each parallel group by its single equivalent resistance.
2
Add the series resistances to give the total resistance.
3
Use I = V/Rtotal to find the supply current.
4
Work back through the circuit, finding the p.d. across the parallel group as I × Rparallel.
5
Find the current in each branch from I = V/R.
Final check
- Final check the branch currents must sum to the total and the p.d.s around each loop must sum to the supply p.d.
Habit
- Habit state the common quantity first: same current in series, same p.d. in parallel
Part 6 of 8Practical effects
Household sockets
- Household sockets they are wired in parallel so each appliance gets the full mains p.d. and can be switched independently
- Adding appliances adds current, so too many on one circuit can overload it.
Series lamps
- Series lamps decorative lights in series all fail when one filament breaks, because the loop is open
Adding a resistor
- Adding a resistor in series it reduces the current, and in parallel it increases the total current drawn from the source
Removing a branch
- Removing a branch for an ideal source the p.d. across the other branches is unchanged,
- so their currents are unchanged and only the total current falls
Part 7 of 8Meters in circuits
Meters in circuits
Meter positions
- Meter positions an ammeter is connected in series and a voltmeter in parallel
Real voltmeter
- Real voltmeter in parallel it slightly reduces the combined resistance and alters the p.d. measured
- A high meter resistance minimises this error.
Real ammeter
- Real ammeter in series it adds a small resistance and slightly lowers the current
Type of error
- Type of error these effects are systematic errors
Part 8 of 8More from the specification
1Electric Current and Charge Carrier Drift
- Electric current I represents the rate of flow of negative electrons through a conductor, described by the transport equation I = n·A·v·q,
- where material resistivity governs overall conduction.
2Electromotive Force and Internal Resistance
- A chemical battery composed of galvanic cells supplies electromotive force ε;
- due to internal resistance r, the terminal potential difference V delivered to an external circuit decreases as current increases, described by the linear equation V = ε - I·r.
3Electrical Power Dissipation
- The electrical power dissipated in a circuit component is calculated using P = I·V = I²·R = V² / R;
- on a power-current graph, power increases parabolically with current.
4Energy transferred
- W = V Q, in joules.What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)
5Circuit diagram
- Drawing of a circuit using standard symbols.
6Light intensity
- How bright the light falling on a surface is.
7Fixed resistor
- Resistor with a resistance that cannot change.
8Conventional current
- Current drawn from the positive to the negative terminal.
9Electron
- Negatively charged particle in an atom.
10Battery
- Two or more cells joined together.
11Resistivity
- Property of a material defined by ρ = RA/L.
12Thermistor
- Resistor whose resistance falls as temperature rises.
13Temperature
- Measure of the average kinetic energy of the particles.
14Conductor
- Material that allows current to flow.
15Internal resistance
- Resistance inside a cell that causes lost p.d.
16Electrical energy
- Energy carried by electrons in a circuit.
Key terms
| Term | Meaning |
|---|---|
| Series | Components in a single loop sharing the same current. |
| Parallel | Components connected across the same two points, sharing the same p.d. |
| Equivalent resistance | Single resistance that would draw the same current from the same supply. |
| Junction | Point where the current splits or combines; the sum of currents in equals the sum out. |
| Kirchhoff's laws | Charge is conserved at a junction; energy is conserved around a loop. |
Avoid these mistakes
1
Adding resistances in parallel instead of adding reciprocals, or forgetting to invert at the end.
2
Thinking the p.d. splits between parallel branches — it is the same across each.
3
Saying adding a resistor in parallel increases the total resistance — it always decreases it.
4
Assuming the current is the same in each parallel branch — it is equal only for equal resistances.
5
Forgetting to use the supply current for the series part when working back through a mixed circuit.
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