Curriculum
Physics
Chapter 1 - Electric Current, Ohms Law and Kirchhoffs Laws
0/20
Chapter 2 - Magnetic Effects of Electric Current and Measuring Instruments
0/223.1Use3.2Construction3.3Action3.4Why the parts are used (typical reasons)3.5Sensitivity3.6The ammeter (shunt)3.7The voltmeter (multiplier)3.8Comparison of ammeter and voltmeter3.9The ohmmeter3.10Using the galvanometer to measure current, emf and resistance3.11Analogue and digital instruments3.12Typical "give reasons" for this chapter3.13Summary of formulas
Chapter 3 - Electromagnetic Induction and AC Dynamo and Transformer
0/24Chapter 4 - Alternating Current AC Circuits
0/301.1Alternating current1.2Advantages of AC1.3The hot-wire ammeter1.4Non-inductive ohmic resistor1.5Pure inductor (coil of zero ohmic resistance)1.6Inductive reactance1.7Capacitor and DC1.8Capacitor and AC1.9Capacitive reactance1.10Combinations of capacitors1.11Key Scientific Tables & Anatomical Diagrams Extracted from Official Curricula1.12📌 Comprehensive Scientific Terminology Dictionary:1.13🔍 In-Depth Explanations, Deductions & Multi-Book Insights:1.14Lesson summary
2.1Impedance2.2Phase relationships in a series circuit2.3R–L series circuit2.4R–C series circuit2.5R–L–C series circuit2.6Power2.7Variation with frequency2.8Worked examples (new values)2.9The oscillating (LC) circuit2.10Resonance2.11Tuning a radio receiver2.12Summary of formulas2.13Key Scientific Tables & Anatomical Diagrams Extracted from Official Curricula2.14📌 Comprehensive Scientific Terminology Dictionary:2.15🔍 In-Depth Explanations, Deductions & Multi-Book Insights:2.16Lesson summary
Chapter 5 - Dual Nature of Wave and Particle
0/331.1Before we start: why "modern" physics?1.2What we already know about light1.3Hot bodies radiate1.4Features of the Planck curve1.5Applications of thermal radiation1.6The black body1.7The failure of classical physics (the "ultraviolet catastrophe")1.8Planck's explanation (1900)1.9Worked examples (Lesson 1)1.10Key Scientific Tables & Anatomical Diagrams Extracted from Official Curricula1.11Lesson 1 - Blackbody Radiation, Planck Hypothesis and Photoelectric Effect1.12Lesson summary
2.1Why electrons stay inside a metal2.2Thermionic emission and the cathode-ray tube (CRT)2.3The photoelectric effect2.4Einstein's explanation (1905)2.5Stopping potential and the graphs2.6Using the energy unit eV2.7Worked examples (Lesson 2)2.8The Compton effect2.9Properties of the photon2.10Radiation force (light pressure)2.11Macroscopic and microscopic models of light2.12Reflection or transmission of photons2.13Worked examples (Lesson 3)2.14De Broglie's idea (1923)2.15Why do we not notice the wave nature of a ball?2.16Wavelength of an accelerated electron2.17The electron microscope2.18Comparison: optical and electron microscope2.19Worked examples (Lesson 4)2.20Chapter summary (key points)2.21Common mistakes to avoid
Chapter 6 - Atomic Spectra and X-Rays
0/281.1Why a new model was needed1.2Bohr's postulates (hydrogen atom)1.3Radii and energies of the hydrogen atom1.4Excitation and emission in hydrogen1.5The series of the hydrogen spectrum1.6Limitations1.7Worked examples (Lesson 1)1.8The spectrometer1.9Types of spectra1.10Worked examples (Lesson 2)1.11What are X-rays?1.12Properties of X-rays1.13Production: the Coolidge tube1.14The X-ray spectrum1.15Origin of the characteristic radiation1.16Origin of the continuous radiation (bremsstrahlung)1.17Comparison of characteristic and continuous X-rays1.18Applications of X-rays1.19Worked examples (Lesson 3)1.20Going deeper — how Bohr's numbers are obtained, and a problem-solving workshop1.21Derivation of the radius and energy (hydrogen)1.22Understanding the energy-level diagram1.23Ionisation, excitation and de-excitation1.24More worked examples1.25X-ray quantities for practice1.26Exam-style reasoning guide1.27Chapter summary1.28Common mistakes
Chapter 7 - Lasers and Principles
0/311.1Energy levels and transitions1.2Comparison between spontaneous and stimulated emission1.3Worked examples (Lesson 1)1.4Properties of the laser beam1.5Monochromaticity (spectral purity)1.6Collimation (a parallel narrow beam)1.7Coherence1.8Intensity (concentration)1.9Worked examples (Lesson 2)1.10Population inversion1.11The three essential elements of any laser1.12Laser action step by step1.13Worked examples (Lesson 3)1.14Construction1.15Operation1.16Applications of lasers1.17Holography (3-D photography)1.18Medicine1.19Other applications1.20Why a threshold? (gain versus loss)1.21Continuous and pulsed operation1.22A guide to common lasers1.23Eye safety and classes1.24Photon arithmetic for laser problems1.25Typical exam questions and model answers (outline)1.26Chapter summary1.27Common mistakes1.28Key Scientific Tables & Anatomical Diagrams Extracted from Official Curricula1.29📌 Comprehensive Scientific Terminology Dictionary:1.30🔍 In-Depth Explanations, Deductions & Multi-Book Insights:1.31Lesson summary
Chapter 8 - Modern Electronics and Semiconductors
0/311.1Conductors, insulators and semiconductors1.2The silicon crystal1.3Free electrons and holes1.4Motion of holes1.5Conduction in a semiconductor compared with a metal1.6Sensitivity of semiconductors1.7Worked examples (Lesson 1)1.8Why dope?1.9n-type semiconductor (donor impurities)1.10p-type semiconductor (acceptor impurities)1.11The law of mass action1.12Summary comparison1.13Worked examples (Lesson 2)1.14Formation of the junction1.15Biasing the junction1.16The diode as a switch and as a rectifier1.17Electronic tuning (the varactor)1.18Worked examples (Lesson 3)1.19Structure1.20Operation (n-p-n, common base)1.21Current ratios1.22The transistor as an amplifier1.23The transistor as a switch (and inverter)1.24Worked examples (Lesson 4)
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0/831.1Key terms1.2Laws and key relationships1.3Boyle's Law and Isothermal Compression Mechanics1.4Charles's Law, Absolute Zero, and the Kelvin Temperature Scale1.5The General Gas Law and Ideal Gas Mixtures1.6Comparison1.7Worked examples1.8Exam tips1.9Key Scientific Tables & Anatomical Diagrams Extracted from Official Curricula1.10🔍 In-Depth Explanations, Deductions & Multi-Book Insights:
2.1Key terms2.2Laws and key relationships2.3Intensive Physics of Density and Non-Contracting Fluid Mixtures2.4Liquid Pressure at Depth and Manometric Measuring Instruments2.5Pascal's Principle and Hydraulic Systems2.6Worked examples2.7Exam tips2.8Real-world applications2.9Key Scientific Tables & Anatomical Diagrams Extracted from Official Curricula2.10📌 Comprehensive Scientific Terminology Dictionary:2.11🔍 In-Depth Explanations, Deductions & Multi-Book Insights:
4.1Key terms4.2Laws and key relationships4.3Torricellian Barometer and Standard Atmospheric Pressure4.4The U-Tube Manometer and Immiscible Fluids Hydrostatic Equilibrium4.5Pascal's Principle and Hydraulic Engineering Systems4.6Comparison4.7Worked examples4.8Exam tips4.9Key Scientific Tables & Anatomical Diagrams Extracted from Official Curricula4.10🔍 In-Depth Explanations, Deductions & Multi-Book Insights:4.11Lesson summary
Text lesson
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits
Overview
Overview
🌳 Concept tree
- Lesson 2 Resistor Combinations and Ohms Law for Closed Circuits
- ├── Combining resistors
- ├── Resistors in series
- ├── Resistors in parallel
- ├── Mixed networks
- ├── Worked examples (new values)
- ├── Ohm's law for a closed circuit
- └── Terminal voltage
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 1 / 9
Combining resistors
Combining resistors
- Resistors are combined in only two basic ways, series and parallel.
- The aim is always the same replace the group by one single equivalent resistance R that would draw the same current from the same source.
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 2 / 9
Resistors in series
Resistors in series
| Comparison aspect | Main idea | Keywords |
|---|---|---|
| Purpose | to obtain a larger resistance than any single resistor | obtainlargerresistancesingle |
| How to measure the equivalent resistance experimentally |
| connectresistorsaftercircuit |
- Facts for a series connection:
- The same current I passes through every resistor (there is only one path, and charge cannot pile up).
- The total voltage is the sum of the individual voltages V = V₁ + V₂ + V₃.
- Derivation Since V = IR, V₁ = IR₁, V₂ = IR₂, V₃ = IR₃. Then IR = IR₁ + IR₂ + IR₃, and dividing by I:
- R = R₁ + R₂ + R₃
| Comparison aspect | Main idea | Keywords |
|---|---|---|
| • |
| equivalentresistancelargerlargest |
| For N equal resistors each of value R₀ | R = N R₀ | |
| The voltage divides in proportion to resistance | V₁ : V₂ : V₃ = R₁ : R₂ : R₃ (the bigger resistor takes the bigger share). This is the potential divider idea: V₁ = V × R₁ / (R₁ + R₂ + R₃) | biggerresistortakesshare |
| Disadvantage | if one component breaks (open circuit) the current stops in all of them. A string of old-fashioned decoration lamps all go out when one lamp burns out for exactly this reason | componentbreaksopencircuit |
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 3 / 9
Resistors in parallel
Resistors in parallel
| Comparison aspect | Main idea | Keywords |
|---|---|---|
| Purpose | to obtain a smaller resistance out of several larger ones | obtainsmallerresistanceseveral |
| How to measure the equivalent resistance experimentally |
| connectthreeresistorsside |
| • | Facts for a parallel connection | Factsparallelconnection |
- The same potential difference V is across every branch (all the branches start at one common point and end at another common point).
- The main current splits I = I₁ + I₂ + I₃.
- Derivation I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃, and I = V/R. Substituting into I = I₁ + I₂ + I₃ and dividing by V:
- 1/R = 1/R₁ + 1/R₂ + 1/R₃
| Comparison aspect | Main idea | Keywords |
|---|---|---|
| For two resistors |
| R₁R₂productoverquicker |
| For N equal resistors | R = R₀ / N | |
| • |
| equivalentresistancesmallersmallest |
| Advantage |
| branchworksindependentlyhousehold |
| • |
| resistorscurrentbranchfound |
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 4 / 9
Mixed networks
Mixed networks
- To find the equivalent resistance of a mixed network, replace each parallel or series group by its equivalent, working step by step from the farthest end towards the source.
- To find individual currents and voltages, work backwards: total current → voltage across each group → current in each branch.
- A reliable method:
- Identify the groups that are clearly series (the same current, with no junction between them) or clearly parallel (the same two end points).
- Replace the innermost group first and redraw a simpler circuit.
- Repeat until one resistor is left; that is R.
- Find the main current from I = V / R (or I = VB / (R + r) if the source has internal resistance).
- voltage across each equivalent resistor = I × its value; then split the current between parallel branches.
- Check by adding the branch currents and by checking that the voltages around the circuit add up to the battery voltage.
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 5 / 9
Worked examples (new values)
Worked examples (new values)
- Example 1 — series. Resistors of 10 Ω, 20 Ω and 30 Ω are in series with a 30 V battery of negligible internal resistance.
- R = 10 + 20 + 30 = 60 Ω. I = 30/60 = 0.5 A in every resistor.
- V₁ = 0.5 × 10 = 5 V, V₂ = 0.5 × 20 = 10 V, V₃ = 0.5 × 30 = 15 V; the sum is 30 V, equal to the battery emf.
- Example 2 — parallel. The same three resistors are connected in parallel across the same battery.
- Each has 30 V across it I₁ = 3 A, I₂ = 1.5 A, I₃ = 1 A, total 5.5 A.
- 1/R = 1/10 + 1/20 + 1/30 = (6 + 3 + 2)/60 = 11/60, so R = 60/11 = 5.45 Ω. Check: 30 / 5.45 = 5.5 A.
- Example 3 — mixed. A 4 Ω and a 12 Ω resistor are in parallel; this pair is in series with a 5 Ω resistor and a 16 V battery (r = 0).
- Parallel pair 4×12 / 16 = 3 Ω. Total R = 3 + 5 = 8 Ω. I = 16/8 = 2 A.
- Voltage across the pair = 2 × 3 = 6 V. So I(4 Ω) = 6/4 = 1.5 A and I(12 Ω) = 6/12 = 0.5 A (sum = 2 A).
- Example 3a — a second series circuit. Three resistors of 8 Ω, 15 Ω and 27 Ω are joined in series across a 60 V supply (negligible internal resistance).
- (a) R = 8 + 15 + 27 = 50 Ω.
- (b) I = 60 / 50 = 1.2 A, the same in all three.
- (c) V₁ = 1.2 × 8 = 9.6 V, V₂ = 1.2 × 15 = 18 V, V₃ = 1.2 × 27 = 32.4 V. Sum = 60 V ✔.
- Notice that the 27 Ω resistor, being the largest, takes the largest share (54%) of the voltage.
- Example 3b — a second parallel circuit. Resistors of 12 Ω, 20 Ω and 30 Ω are connected in parallel across a 24 V battery with negligible internal resistance.
- (a) Each branch has 24 V I₁ = 24/12 = 2 A, I₂ = 24/20 = 1.2 A, I₃ = 24/30 = 0.8 A.
- (b) The main current is I = 2 + 1.2 + 0.8 = 4 A.
- (c) 1/R = 1/12 + 1/20 + 1/30 = (5 + 3 + 2)/60 = 10/60, so R = 6 Ω; check: 24/6 = 4 A ✔.
- (d) R = 6 Ω is smaller than the smallest resistor (12 Ω), as it must be.
| Comparison aspect | Main idea | Keywords |
|---|---|---|
| Example 3c — a mixed circuit with the parallel group at the end. |
| resistorpairseriescombination |
| Step 1 | parallel pair = 20 × 5 / 25 = 4 Ω | parallelpair |
| Step 2 | R = 4 + 6 = 10 Ω | |
| Step 3 | I = 15 / 10 = 1.5 A (this is also the current in the 6 Ω resistor) | currentresistor |
| Step 4 | voltage across the pair = 1.5 × 4 = 6 V | voltageacrosspair |
| Step 5 |
| |
| Example 3d — a series group inside a parallel group. |
| resistorformbranchpair |
| Step 1 | the series branch = 6 + 12 = 18 Ω | seriesbranch |
| Step 2 | parallel with 9 Ω = 18 × 9 / 27 = 6 Ω | parallel |
| Step 3 |
| |
| Step 4 |
| voltageacrossparallelpart |
| Step 5 |
| branchresistor |
| Step 6 | the voltage across the 6 Ω resistor is 0.667 × 6 = 4 V and across the 12 Ω resistor is 8 V | voltageacrossresistor |
Example 3e — equal resistors.→Five identical 10 Ω resistors are connected (i) in series and (ii) in parallel. (i) R = 5 × 10 = 50 Ω. (ii) R = 10 / 5 = 2 Ω. The ratio of the two combinations is 25 : 1.
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 6 / 9
Ohm’s law for a closed circuit
Ohm’s law for a closed circuit
- A real source has an internal resistance r (the resistance of the electrolyte, plates, wires, etc.
- inside the cell).
- The current passes through the external resistance R and the internal resistance r in series.
- The emf equals the total work per coulomb round the whole circuit (outside plus inside the source), so
- VB = I R + I r = I (R + r)
- I = VB / (R + r)
This is Ohm’s law for a closed circuitthe current equals the total emf divided by the total (external + internal) resistance of the circuit.
In wordstotal emf over total resistance.
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 7 / 9
Terminal voltage
Terminal voltage
- The voltage across the terminals of the source while it delivers current is
V = VB − I r (and also V = I R)
| Comparison aspect | Main idea | Keywords |
|---|---|---|
| The term I r is the "lost volts" |
| energycoulombusedinside |
| • | If the circuit is open (I = 0) the voltmeter across the source reads V = VB. This gives another definition: the emf of a source is the potential difference across its terminals when no current is flowing in the circuit. | circuitopenvoltmeteracross |
| • | As the external resistance R is increased (for example by moving a rheostat), I falls, I r falls, and the terminal voltage rises towards VB. As R is decreased (towards a short circuit) the current becomes large (VB / r), and the terminal voltage drops towards zero. | externalresistanceincreasedexample |
| • | A voltmeter of very high resistance across the terminals reads (almost exactly) the emf only when the circuit is open | voltmeterveryhighresistance |
| • | Internal resistance can be found from r = (VB − V) / I. | Internalresistancefound |
| Experiment idea (the book’s Fig 1-5) | connect a cell, a rheostat, an ammeter and a switch in series, with a voltmeter across the cell. With the switch open the voltmeter reads the emf. Close the switch and the reading drops to V = VB − I r. Increasing the rheostat resistance lowers I and brings the reading back towards VB, which shows how V and I are related by a straight line. | connectcellrheostatammeter |
| Short circuit | when the external resistance is zero, I = VB / r. Because r is small the current is very large; this can overheat and damage the source and the wires, and it is why fuses and circuit breakers are used. | externalresistancezeroBecause |
| Charging | if a source is forced to carry current in the opposite direction (current entering its positive terminal, as when a battery is being recharged by a stronger source), the terminal voltage is V = VB + I r, greater than the emf. | sourceforcedcarrycurrent |
| Example 4. | A cell of emf 6 V and internal resistance 0.4 Ω is connected to an external resistor of 11.6 Ω | cellinternalresistanceconnected |
| • | I = 6 / (11.6 + 0.4) = 0.5 A. Terminal voltage V = 6 − 0.5 × 0.4 = 5.8 V (= 0.5 × 11.6) | Terminalvoltage |
| Example 4a — a second case. | A battery of emf 9 V and internal resistance 0.5 Ω supplies a 4 Ω resistor | batteryinternalresistancesupplies |
| Step 1 | total resistance = 4 + 0.5 = 4.5 Ω | totalresistance |
| Step 2 | I = 9 / 4.5 = 2 A | |
| Step 3 | V = VB − I r = 9 − 2 × 0.5 = 8 V (check: I R = 2 × 4 = 8 V ✔) | check |
| Step 4 | lost volts = 1 V | lostvolts |
| Example 4b — finding the internal resistance. | A battery of emf 12 V is connected to a resistor. A high-resistance voltmeter across the battery reads 11 V while a current of 2 A flows. Then r = (VB − V) / I = (12 − 11) / 2 = 0.5 Ω, and the external resistance is R = V / I = 11 / 2 = 5.5 Ω. | batteryconnectedresistorhigh |
| Example 4c — emf and r from two readings. | A cell gives a current 1.0 A when connected to a 4 Ω resistor and 0.5 A when connected to a 10 Ω resistor. Find r and VB. | cellgivescurrentconnected |
| • | VB = 1.0 (4 + r) = 0.5 (10 + r) | |
| • |
| giving |
| • | Then VB = 1.0 × (4 + 2) = 6 V | Then |
| • | Check with the second reading: 0.5 × 12 = 6 V ✔ | Checksecondreading |
| Example 4d — short-circuit current. | A 1.5 V cell has an internal resistance 0.25 Ω. If its terminals are joined by a thick wire (R ≈ 0) the current is 1.5 / 0.25 = 6 A. Compare this with the 0.3 A it delivers to a 4.75 Ω lamp: 1.5 / (4.75 + 0.25) = 0.3 A | cellinternalresistanceterminals |
| Example 4e — effect of changing R on the voltmeter. |
| batterycircuitopenreading |
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 8 / 9
Part 9
Part 9
- 📖
🔍 In-Depth Explanations, Deductions & Multi-Book Insights:
Physics Thanaweya Amma (2026/2027)
- Lesson 2 – Resistor Combinations and Ohms Law for Closed Circuits
- Resistors can be connected in series (to increase equivalent resistance with constant current) or parallel (to decrease equivalent resistance with constant voltage).
- Ohm's Law for Closed Circuits calculates the terminal voltage of a non-ideal battery (V = VB – I·r).
🌳 Hierarchy Classification & Concept Tree
Resistor Networks and Closed Circuits
├── 1. Series Resistor Combination
│ ├── Constant currentItotal = I1 = I2 = I3
│ ├── Divided voltageVtotal = V1 + V2 + V3
│ └── Equivalent resistanceReq = R1 + R2 + R3
├── 2. Parallel Resistor Combination
│ ├── Constant voltageVtotal = V1 = V2 = V3
│ ├── Divided currentItotal = I1 + I2 + I3
│ └── Equivalent resistance1/Req = 1/R1 + 1/R2 + 1/R3 (Req is smaller than smallest resistor)
└── 3. Ohm's Law for Closed Circuits
├── I = VB / (Rexternal + rinternal)
├── Battery Terminal Voltage (Discharging)V = VB – I·r
└── Battery Terminal Voltage (Charging)V = VB + I·r
📋 Master Teacher's Blackboard & Exam Secrets
| Comparison aspect | Main idea | Keywords |
|---|---|---|
| RULE 1 |
| batterydischargingterminalvoltage |
| RULE 2 |
| Terminalvoltageequalscircuit |
| RULE 3 |
| externalresistancedecreasescurrent |
| RULE 4 |
| batterybeingrechargedexternal |
| 📊 Comparative Analysis | Comparative Synthesis: Series vs. Parallel Resistor Networks | SynthesisSeriesParallelResistor |
| Feature | Series Combination | Parallel Combination |
|---|---|---|
| Main Purpose | To obtain a large equivalent resistance | To obtain a small equivalent resistance |
| Current Intensity | Same constant current flows through all | Current branches inversely with resistance |
| Potential Difference | Voltage divides directly with resistance | Potential difference is identical across all |
| Equivalent Resistance | Req = Σ Ri (larger than largest) | 1/Req = Σ 1/Ri (smaller than smallest) |
| Failure of one bulb | Entire circuit shuts off completely | Other branches continue operating independently |
Lesson 2: Resistor Combinations and Ohms Law for Closed Circuits · 9 / 9
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