[!caution] SUPERSEDED This page has been merged into FAD1022 Final Exam Scope — Complete Guide (2026-05-04) along with new exam-tip data. Kept for reference; do not use as primary revision source.

FAD1022 Exam Structure — Detailed Leak

[!warning] Exam Structure Leak — Use Strategically This details the section-by-section breakdown from leaked information. Verify against your actual exam briefing. Topics and marks may vary. Use this as a structural blueprint for time allocation and question selection strategy — not as a substitute for mastering the material.

Exam Overview

Section	Format	Max Marks	Effective Marks	Time Suggestion
A	15 structured × 3 marks	45	45 (all compulsory)	~30 min
B	4 structured Q × 12 marks → pick 3	48	36	~55 min
C	6 structured Q × 12 marks → pick 4	72	48	~75 min
Total		165	~129	~2h 40min

[!tip] Marks Efficiency You attempt 15 + 3 + 4 = 22 questions worth ≈129 marks. Section C carries the most weight (37%) so prioritise accuracy there.

Section A — Structured Questions (15 × 3 = 45 marks)

All questions compulsory. 2–3 minutes per question.

Topics Breakdown

#	Topic	What to Study	Leak Notes
A1	Capacitor Charging & Discharging	$q(t) = Q_0(1 - e^{-t/\tau})$, $q(t) = Q_0 e^{-t/\tau}$, $\tau = RC$, time constant graphs, energy $U = \frac12 CV^2$	Standard RC transient behaviour — be able to read graphs and compute $q$, $i$, $V$ at $t=1\tau, 3\tau, 5\tau$
A2	Kirchhoff's Current Law	$\sum I_{\text{in}} = \sum I_{\text{out}}$; given $\Sigma I = I_1 + I_2 + I_3 = 0$, solve for unknown branch current	Junction rule only (KCL), not KVL. Simple node analysis
A3	Amplifier Formula (ingat/remember)	Op-amp configurations: inverting ($V_{\text{out}} = -\frac{R_f}{R_{\text{in}}} V_{\text{in}}$), non-inverting ($V_{\text{out}} = (1 + \frac{R_f}{R_{\text{in}}}) V_{\text{in}}$), summing, difference	"Ingat" = just remember/memorise the formula. Likely a direct plug-and-chug
A4	Ampere's Law — Long Wire ($r < R$)	$B(r) = \frac{\mu_0 I r}{2\pi R^2}$ (inside wire), $B(r) = \frac{\mu_0 I}{2\pi r}$ (outside). Derivation using $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$	Amperian loop inside the wire: current density $J = I/\pi R^2$, enclosed current $I_{\text{enc}} = J \cdot \pi r^2 = I r^2/R^2$
A5	Lenz Law	—	🚫 NOT TESTED — skip entirely for Section A

Quick-Fire Section A Drill

Capacitor: $C = \kappa \epsilon_0 A/d$, series: $1/C_{\text{eq}} = 1/C_1 + 1/C_2$, parallel: $C_{\text{eq}} = C_1 + C_2$
Kirchhoff: $\sum I = 0$ at a node → $I_1 + I_2 + I_3 = 0$ means some currents are negative (flowing out)
Amplifier: Inverting gain $A_v = -R_f/R_i$; Non-inverting gain $A_v = 1 + R_f/R_i$
Ampere inside wire: $B \propto r$ for $r < R$; $B \propto 1/r$ for $r > R$
Lenz: DO NOT STUDY for Section A ❌

Key Formulas to Memorise for Section A

Concept	Formula
Charging capacitor	$q(t) = CV(1 - e^{-t/RC})$
Discharging capacitor	$q(t) = Q_0 e^{-t/RC}$
RC time constant	$\tau = RC$
Energy stored	$U = \frac12 CV^2$
KCL at a node	$\sum I_{\text{in}} = \sum I_{\text{out}}$
Inverting op-amp	$V_{\text{out}} = -\frac{R_f}{R_{\text{in}}} V_{\text{in}}$
Non-inverting op-amp	$V_{\text{out}} = \left(1 + \frac{R_f}{R_{\text{in}}}\right) V_{\text{in}}$
Ampere's law	$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$
B inside wire ($r < R$)	$B = \frac{\mu_0 I r}{2\pi R^2}$
B outside wire ($r > R$)	$B = \frac{\mu_0 I}{2\pi r}$

Section B — Choose 3 of 4 (4 Q × 12 marks, pick 3 = 36 marks)

[!tip] Selection Strategy Read all 4 questions in the first 3 minutes. Identify which 3 you are most confident in and answer those. The 4th is a safety net.

B1: Electrostatics — E Vector & Projectile Motion

Leak keywords: E vector, Motion with projectile

What They Can Ask (Parts a, b, c — 12 marks total)

Part	Likely Content	Marks (est.)
(a)	Electric field as a vector — superposition of two or more point charges, find $\vec{E}_{\text{net}}$ at a point	4
(b)	Force on a test charge placed at that point: $\vec{F} = q\vec{E}$	3
(c)	Projectile motion in a uniform E-field (charged particle entering between parallel plates) — find deflection, exit velocity, angle	5

Detailed Prep Notes

Electric Field Superposition (Vector)
- For each source charge $Q_i$: $\vec{E}_i = \dfrac{kQ_i}{r_i^2} \hat{r}_i$
- $\hat{r}_i$ points from $Q_i$ to the test point
- Resolve into components: $E_x = \sum E_{ix}$, $E_y = \sum E_{iy}$
- Magnitude: $|\vec{E}_{\text{net}}| = \sqrt{E_x^2 + E_y^2}$
- Direction: $\theta = \tan^{-1}(E_y/E_x)$
- Sign convention: $+Q$ produces field away, $-Q$ produces field toward
Projectile in E-Field
- Setup: charged particle ($q$, $m$) enters horizontally at $v_0$ between plates with uniform $\vec{E}$ (downward for $+$ plate on top)
- Horizontal: $a_x = 0$, $v_x = v_0$, $x = v_0 t$
- Vertical: $F_y = qE$, $a_y = qE/m$ (upward if $q > 0$ and $\vec{E}$ points down = careful with signs!)
- $v_y = a_y t$, $y = \frac12 a_y t^2$
- Deflection at exit: $y = \frac12 \cdot \frac{qE}{m} \cdot \left(\frac{L}{v_0}\right)^2$ where $L$ = plate length
- Exit angle: $\theta = \tan^{-1}(v_y/v_x)$
- Resultant speed: $v = \sqrt{v_0^2 + v_y^2}$
Common Pitfalls
- ❌ Forgetting to treat $\vec{E}$ as a vector (must do components)
- ❌ Sign errors: negative charge deflects opposite to field direction
- ❌ Mixing up $k = 1/(4\pi\epsilon_0) = 9 \times 10^9$ with $\epsilon_0 = 8.85 \times 10^{-12}$

B2: Capacitor + Dielectric + DC

Leak keywords: Parts a&b: Capacitance formula and energy; Part c: Voltage divider (loaded/unloaded) series problem solving

What They Can Ask (Parts a, b, c — 12 marks total)

Part	Likely Content	Marks (est.)
(a)	Capacitance with dielectric: $C = \kappa \epsilon_0 A/d$ — compute $C$ given geometry	3
(b)	Energy stored: $U = \frac12 CV^2 = \frac{Q^2}{2C} = \frac12 QV$ — compute energy, find $Q$, or find $V$	4
(c)	Voltage divider — loaded vs unloaded, series capacitor/resistor network problem solving	5

Detailed Prep Notes

Capacitance & Dielectric (Parts a & b)
- Parallel plate (vacuum): $C_0 = \epsilon_0 A/d$
- With dielectric: $C = \kappa C_0$
- Dielectric insertion scenarios:
  - Battery connected ($V$ constant): $Q$ increases by $\kappa$, $C$ increases by $\kappa$, $E$ unchanged
  - Battery removed ($Q$ constant): $V$ decreases by $\kappa$, $C$ increases by $\kappa$, $E$ decreases by $\kappa$
- Energy: $U = \frac12 CV^2$. When dielectric inserted:
  - $V$ constant → $U$ increases by $\kappa$ (battery does work)
  - $Q$ constant → $U$ decreases by $1/\kappa$ (field does work on dielectric)
Voltage Divider (Part c — Loaded vs Unloaded)
- Unloaded voltage divider: $$V_{\text{out}} = V_{\text{in}} \cdot \frac{R_2}{R_1 + R_2}$$
- Loaded voltage divider (load resistor $R_L$ across $R_2$): $$R_{\text{eq}} = R_2 \parallel R_L = \frac{R_2 R_L}{R_2 + R_L}$$ $$V_{\text{out}} = V_{\text{in}} \cdot \frac{R_{\text{eq}}}{R_1 + R_{\text{eq}}}$$
- Loading effect: $V_{\text{out}}$ drops when load is connected (lower than unloaded value)
- Rule of thumb: loading is negligible when $R_L \gg R_2$ (at least 10×)
Capacitor Voltage Divider (Series Capacitors)
- For two capacitors in series across $V$: $$Q = C_{\text{eq}} V = \frac{C_1 C_2}{C_1 + C_2} \cdot V$$ $$V_1 = \frac{Q}{C_1} = V \cdot \frac{C_2}{C_1 + C_2}, \quad V_2 = V \cdot \frac{C_1}{C_1 + C_2}$$
- Voltage divides inversely to capacitance (smaller $C$ gets larger $V$)

B3: AC — PRC + PLC + PCC

Leak keywords: Phasor diagram, degree, 90°

What They Can Ask (12 marks)

Part	Likely Content	Marks (est.)
(a)	Phasor diagram drawing — PRC (resistive), PLC (inductive), PCC (capacitive) — show $V_R$, $V_L$, $V_C$ and phase angles	4
(b)	Power calculations: $P_e$ (real), $P_{LC}$ (inductive reactive), $P_{CC}$ (capacitive reactive)	4
(c)	Phase angle $\phi$, power factor $\cos\phi$, lead/lag identification	4

Detailed Prep Notes

PRC — Pure Resistive Circuit ($\phi = 0^\circ$)
- $V$ and $I$ in phase
- Phasor: $V_R$ on $0^\circ$ axis, $I$ on $0^\circ$ axis (overlap)
- Power: $P_e = V_{\text{rms}} I_{\text{rms}}$ (all real, no reactive)
- Power factor $\cos\phi = 1$
PLC — Pure Inductive Circuit ($\phi = +90^\circ$)
- $V$ leads $I$ by $90^\circ$
- Phasor: $V_L$ pointing up ($+90^\circ$), $I$ on $0^\circ$
- Reactance: $X_L = \omega L = 2\pi f L$
- Power: $P_e = 0$, $P_{LC} = V_{\text{rms}} I_{\text{rms}} = I_{\text{rms}}^2 X_L$
- CIVIL mnemonic: In an Inductor, V leads I — "I before V, L after C" alphabetically
PCC — Pure Capacitive Circuit ($\phi = -90^\circ$)
- Current leads voltage by $90^\circ$
- Phasor: $V_C$ pointing down ($-90^\circ$), $I$ on $0^\circ$
- Reactance: $X_C = 1/(\omega C) = 1/(2\pi f C)$
- Power: $P_e = 0$, $P_{CC} = V_{\text{rms}} I_{\text{rms}} = I_{\text{rms}}^2 X_C$
- CIVIL mnemonic: In a Capacitor, I leads V — "C before L, I before V"
Phasor Diagram Construction
- Draw horizontal reference axis ($0^\circ$) for current $I$
- $V_R$: along $0^\circ$, length $\propto IR$
- $V_L$: at $+90^\circ$, length $\propto I X_L$
- $V_C$: at $-90^\circ$, length $\propto I X_C$
- Resultant: $V_T = \sqrt{V_R^2 + (V_L - V_C)^2}$
- Phase angle: $\phi = \tan^{-1}\left(\frac{V_L - V_C}{V_R}\right)$
Power Triangle
- Real power $P_e$: horizontal leg
- Net reactive power $P_R = |P_{LC} - P_{CC}|$: vertical leg
- Apparent power $P_A = \sqrt{P_e^2 + P_R^2}$: hypotenuse
- $\cos\phi = P_e / P_A$ (power factor)

B4: AC — Claims & RLC

Leak keywords: 4 claims: select 2 wrong and rewrite; RLC circuit: find 2 parallel ones; Make circuit resonance

What They Can Ask (Parts a, b, c — 12 marks)

Part	Likely Content	Marks (est.)
(a)	4 claims about AC circuits — select 2 that are wrong and rewrite them correctly	4
(b)	RLC circuit diagram — identify the 2 parallel components (likely $L$ and $C$ in parallel, or $R$ in series with parallel $LC$)	3
(c)	Make the circuit resonate — determine what component value ($L$ or $C$) to change to achieve resonance	5

Detailed Prep Notes

Spotting Wrong Claims (Part a)
- Common wrong claims to watch for:
  - ❌ "At resonance, impedance is maximum" → Correct: impedance is minimum ($Z = R$)
  - ❌ "At resonance, current is minimum" → Correct: current is maximum ($I = V/R$)
  - ❌ "Power factor at resonance is 0" → Correct: power factor = 1 (unity)
  - ❌ "In a pure inductor, current leads voltage by 90°" → Correct: voltage leads current by 90°
  - ❌ "In a pure capacitor, voltage leads current by 90°" → Correct: current leads voltage by 90°
  - ❌ "Adding a capacitor always decreases power factor" → Correct: adding a capacitor to an inductive circuit increases PF
  - ❌ "RMS voltage = peak voltage × √2" → Correct: $V_{\text{rms}} = V_0 / \sqrt{2}$ (divides by √2, not multiplies)
  - ❌ "Reactance is independent of frequency" → Correct: $X_L \propto f$, $X_C \propto 1/f$
Identifying Parallel Components in RLC (Part b)
- Look for circuit diagrams. Common configurations:
  - Series RLC: $R$, $L$, $C$ all in series
  - Parallel RLC: $R$, $L$, $C$ all in parallel
  - Mixed: $R$ in series with parallel $LC$ tank circuit
- The leak says "find 2 parallel ones" — likely identifying that $L$ and $C$ are in parallel with each other (the tank circuit), while $R$ is in series
- For parallel $LC$: at resonance, impedance is maximum (opposite of series)
Making the Circuit Resonate (Part c)
- Resonance condition: $X_L = X_C$
- $\omega_0 L = \frac{1}{\omega_0 C}$ → $\omega_0 = \frac{1}{\sqrt{LC}}$
- To resonate at a given frequency:
  - Find required $L$: $L = \frac{1}{\omega_0^2 C}$
  - Find required $C$: $C = \frac{1}{\omega_0^2 L}$
- For series RLC at resonance:
  - $Z = R$ (minimum), $I = V/R$ (maximum)
  - $V_L = V_C$ (they cancel), $V_R = V_{\text{source}}$
- For parallel RLC at resonance:
  - $Z = R$ (maximum for parallel, if $R$ is in parallel too), $I = V/R$ (minimum total current from source)
  - Tank circuit circulates current internally

Which 3 Questions to Choose in Section B

Question	Difficulty	Recommended For	Why
B1: Electrostatic	Medium	Everyone	Standard vector + projectile — predictable and formulaic
B2: Capacitor + DC	Medium	Everyone	Parts a&b are free marks; part c tests voltage divider which is well-defined
B3: AC Phasor + Power	Medium-Hard	Those comfortable with phasors	PRC/PLC/PCC definitions and power triangle are memorisable; phasor drawing requires practice
B4: AC Claims + RLC	Hard	Strong students only	Subjective (spotting wrong claims), needs deep conceptual understanding of RLC

[!tip] Recommended Drop: B4 Unless you are very confident with AC theory, skip B4 — B1, B2, B3 are more predictable and formula-driven.

Section C — Choose 4 of 6 (6 Q × 12 marks, pick 4 = 48 marks)

[!tip] Selection Strategy You must answer 4 out of 6. Pre-select your 4 based on strengths before the exam. If an unexpected question appears, you have 2 backups. Don't switch horses mid-exam.

C1: Magnetism — Derivation (Gauss & Ampere)

Leak keywords: Derivation (Gauss & Ampere) from past years; Focus on 4-wire systems (LT4 has 3-wire); "Please look at sphere"

Detailed Prep Notes

Gauss's Law for Magnetism (Derivation)
- $\oint \vec{B} \cdot d\vec{A} = 0$
- Physical meaning: Magnetic monopoles do not exist; magnetic field lines form closed loops
- True for any closed surface — flux in = flux out
- Derivation typically: start with $\vec{B}$ from a dipole → integrate over closed surface → show net flux = 0
- "Please look at sphere" → probably a spherical Gaussian surface problem:
  - For a point magnetic dipole at centre of sphere: field lines enter one hemisphere and exit the other → net flux = 0
  - This demonstrates $\oint \vec{B} \cdot d\vec{A} = 0$
Ampere's Law (Derivation)
- $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$
- Derivation steps for long straight wire:
  1. Choose an Amperian loop (circular, radius $r$, centred on wire)
  2. By symmetry, $\vec{B}$ is tangential and constant magnitude on loop
  3. $\oint \vec{B} \cdot d\vec{l} = B \cdot 2\pi r$
  4. $I_{\text{enc}} = I$ (for $r > R$) or $I_{\text{enc}} = I \cdot \frac{r^2}{R^2}$ (for $r < R$)
  5. Equate: $B \cdot 2\pi r = \mu_0 I_{\text{enc}}$
  6. Solve: $B = \frac{\mu_0 I}{2\pi r}$ (outside) or $B = \frac{\mu_0 I r}{2\pi R^2}$ (inside)
4-Wire Systems (Focus!)
- LT4 (tutorial/lab test 4) has a 3-wire problem — exam focuses on 4-wire
- Typical problem: Four parallel wires arranged in a square/rectangle, carrying currents in various directions
- Steps:
  1. For each wire, find $\vec{B}$ at the point of interest using $B = \mu_0 I / (2\pi r)$
  2. Determine direction using right-hand grip rule (thumb = current, fingers = $\vec{B}$)
  3. Resolve $\vec{B}$ from each wire into $x$ and $y$ components
  4. Sum vectorially: $\vec{B}_{\text{net}} = \sum \vec{B}_i$
- Common arrangement: 2 wires with current going in, 2 wires with current coming out (makes a magnetic field at centre)
- At centre of square: fields from opposite wires may cancel/combine depending on current directions
Key Differences: 3-wire vs 4-wire
- 3-wire (LT4): triangle arrangement → easier symmetry
- 4-wire: square arrangement → need more careful vector resolution
- Practice: Find $\vec{B}$ at the centre of a square of side $a$ with currents $I$ in each corner, all going into page

C2: Electromagnetism — AC Motor (Torque)

Leak keywords: AC motor (Torque)

Detailed Prep Notes

Torque on a Current Loop in a Magnetic Field
- $\vec{\tau} = \vec{\mu} \times \vec{B}$ where $\vec{\mu} = NIA\hat{n}$ (magnetic dipole moment)
- Magnitude: $\tau = NIAB\sin\theta$ where $\theta$ = angle between $\hat{n}$ (loop normal) and $\vec{B}$
- $N$ = number of turns, $I$ = current, $A$ = area of loop
AC Motor Operation
- A current-carrying loop in a magnetic field experiences torque, causing rotation
- In an AC motor, the current alternates direction, so torque always acts in the same rotational direction
- Key formula: $\tau(t) = NIAB\sin(\omega t)$
- Average torque: $\tau_{\text{avg}} = \frac{2}{\pi} NIAB$ (for a full cycle)
Typical Problem Parts
- (a) Derive expression for torque on a rectangular loop in a uniform B-field
- (b) Calculate maximum torque given $N$, $I$, $A$, $B$
- (c) Explain how the motor maintains rotation (commutator / AC alternation)
Formulas to Know
- Magnetic moment: $\mu = NIA$
- Torque: $\tau = \mu B \sin\theta = NIAB\sin\theta$
- Work done by motor: $W = \tau \cdot \Delta\theta$
- Power: $P = \tau \omega$

C3: Transformer — Self & Mutual Induction

Leak keywords: Self and Mutual induction

Detailed Prep Notes

Self-Inductance
- $V_L = -L \frac{dI}{dt}$ (Faraday's law for inductor)
- For a solenoid: $L = \frac{\mu_0 N^2 A}{l}$
- Energy stored in inductor: $U = \frac12 L I^2$
- Time constant in RL circuit: $\tau = L/R$
Mutual Inductance
- $V_2 = -M \frac{dI_1}{dt}$ (voltage induced in coil 2 due to changing current in coil 1)
- $M = k\sqrt{L_1 L_2}$ where $k$ = coupling coefficient ($0 \le k \le 1$)
- For ideal transformer ($k=1$): $M = \sqrt{L_1 L_2}$
- Reciprocity: $M_{12} = M_{21} = M$
Ideal Transformer
- Voltage ratio: $\frac{V_2}{V_1} = \frac{N_2}{N_1} = n$ (turns ratio)
- Current ratio: $\frac{I_2}{I_1} = \frac{N_1}{N_2} = \frac{1}{n}$
- Power: $V_1 I_1 = V_2 I_2$ (ideal, no losses)
- Step-up: $N_2 > N_1$, $V_2 > V_1$, $I_2 < I_1$
- Step-down: $N_2 < N_1$, $V_2 < V_1$, $I_2 > I_1$
Typical Problem Parts
- (a) Define self-inductance and derive $L = \mu_0 N^2 A / l$
- (b) Define mutual inductance — two coils, find $M$ given geometry or $V_2$ given $dI_1/dt$
- (c) Transformer problem — given $N_1$, $N_2$, $V_1$, find $V_2$ and $I_2$ for a resistive load
Derivation of Self-Inductance of a Solenoid
- $B = \mu_0 n I = \mu_0 (N/l) I$
- Flux through one turn: $\Phi_B = BA = \mu_0 NIA/l$
- Total flux linkage: $N\Phi_B = \mu_0 N^2 IA/l$
- $L = N\Phi_B / I = \mu_0 N^2 A/l$

C4: Semiconductor & Biasing

Leak keywords: Clipper/rectifier wave; Voltage divider (C) → why more stable; Comparison: Fixed emitter vs Emitter stabilized (Ic vs Vce); Why relates to IE and IB (IE = IB + IC); Calculation for IB; Change in Beta has no effect

Detailed Prep Notes

Clipper / Rectifier Wave (Bukit/Hill Shape)
- Clipper: removes portion of input waveform above/below a threshold voltage
- Rectifier: converts AC to DC
  - Half-wave: only positive half-cycle passes
  - Full-wave: both half-cycles rectified (using bridge rectifier or centre-tapped transformer)
- "Bukit/hill shape" = the output waveform looks like a series of hills (half-wave rectified sine wave)
- Know how to draw input vs output waveforms for:
  - Half-wave rectifier
  - Full-wave bridge rectifier
  - Positive/negative clipper circuits
Voltage Divider Bias (Configuration C) — Why More Stable
- Voltage divider bias uses $R_1$ and $R_2$ to set base voltage $V_B$ independently of $\beta$
- $V_B = V_{CC} \cdot \frac{R_2}{R_1 + R_2}$ (independent of transistor parameters!)
- $V_E = V_B - V_{BE}$, $I_E = V_E/R_E$, $I_C \approx I_E$
- Why more stable: $V_B$ is fixed by resistor divider, not by $\beta$. If $\beta$ changes (due to temperature), $I_B$ adjusts automatically to keep $I_C$ roughly constant
- Compared to fixed bias: fixed bias has $I_B = (V_{CC} - V_{BE})/R_B$, so $I_C = \beta I_B$ varies directly with $\beta$

Comparison: Fixed Emitter vs Emitter-Stabilized ($I_C$ vs $V_{CE}$)

Parameter	Fixed Bias	Emitter-Stabilized Bias	Voltage Divider Bias
$I_B$ formula	$\frac{V_{CC} - V_{BE}}{R_B}$	$\frac{V_{CC} - V_{BE}}{R_B + (\beta+1)R_E}$	$I_B = \frac{V_B - V_{BE}}{R_B}$
$I_C$ formula	$\beta I_B$	$\beta I_B$	$I_C = \frac{V_B - V_{BE}}{R_E/\beta + R_E/\beta}$
Q-point stability vs $\beta$	Poor (directly proportional)	Moderate ($R_E$ provides negative feedback)	Best ($V_B$ fixed independently)
$V_{CE}$ formula	$V_{CC} - I_C R_C$	$V_{CC} - I_C(R_C+R_E)$	$V_{CC} - I_C(R_C+R_E)$
$I_{C(\text{sat})}$	$V_{CC}/R_C$	$V_{CC}/(R_C+R_E)$	$V_{CC}/(R_C+R_E)$

Why $I_E = I_B + I_C$? (KCL at Transistor)
- Current entering the transistor (emitter) = current leaving (base + collector)
- $I_E = I_B + I_C$ — fundamental KCL applied to the transistor as a node
- Since $I_C = \beta I_B$, we have $I_E = I_B + \beta I_B = (\beta + 1)I_B$
- This relationship is used to find $I_B$ when $I_E$ is known, and vice versa
Calculation for $I_B$
- Fixed bias: $I_B = \dfrac{V_{CC} - V_{BE}}{R_B}$
- Emitter-stabilized: $I_B = \dfrac{V_{CC} - V_{BE}}{R_B + (\beta + 1)R_E}$
- Voltage divider: First find $V_B = V_{CC}\frac{R_2}{R_1+R_2}$, then $I_B = \dfrac{V_B - V_{BE}}{R_B}$ (approx) or more precisely: $I_B = \dfrac{V_B - V_{BE}}{R_B + (\beta+1)R_E}$ where $R_B = R_1 \parallel R_2$
Change in Beta Has No Effect — Why?
- In voltage divider bias (and to a lesser extent, emitter-stabilized), the Q-point is designed to be $\beta$-independent
- Because $V_B$ is set by the divider, $V_E = V_B - V_{BE}$ is fixed, so $I_E = V_E/R_E$ is fixed
- Since $I_C \approx I_E$, collector current is nearly independent of $\beta$
- This is the key advantage: stable Q-point despite $\beta$ variation
- Expected exam question: "Explain why changing $\beta$ has negligible effect on $I_C$ in a voltage divider bias circuit"

C5: Atomic Physics — Derivation of Radius

Leak keywords: Part (c): Derivation of radius

Detailed Prep Notes

Bohr Radius Derivation (Full Derivation)
- Postulates of Bohr model:
  1. Electrons orbit nucleus in circular orbits (Coulomb force = centripetal force)
  2. Angular momentum is quantized: $m_e v r_n = n\hbar$ where $n = 1, 2, 3, \dots$
  3. Electrons emit/absorb photons when jumping between orbits: $\Delta E = hf = E_i - E_f$
- Derivation step-by-step:
  1. Coulomb force = centripetal force: $$\frac{1}{4\pi\epsilon_0} \frac{e^2}{r_n^2} = \frac{m_e v_n^2}{r_n}$$
  2. Quantization of angular momentum: $$m_e v_n r_n = n\hbar$$
  3. Solve for $v_n$ from (2): $v_n = \dfrac{n\hbar}{m_e r_n}$
  4. Substitute into (1): $$\frac{1}{4\pi\epsilon_0} \frac{e^2}{r_n^2} = m_e \cdot \frac{n^2 \hbar^2}{m_e^2 r_n^2} \cdot \frac{1}{r_n}$$
  5. Simplify: $$\frac{e^2}{4\pi\epsilon_0 r_n^2} = \frac{n^2 \hbar^2}{m_e r_n^3}$$
  6. Solve for $r_n$: $$\boxed{r_n = \frac{4\pi\epsilon_0 n^2 \hbar^2}{m_e e^2} = n^2 a_0}$$
  7. Bohr radius ($n=1$): $$\boxed{a_0 = r_1 = \frac{4\pi\epsilon_0 \hbar^2}{m_e e^2} = 0.529 \times 10^{-10}\ \text{m} = 0.529\ \text{Å}}$$
Energy Levels (Often asked after radius)
- Total energy: $E_n = -\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{2r_n}$
- Using $r_n$: $E_n = -\frac{m_e e^4}{8\epsilon_0^2 h^2} \cdot \frac{1}{n^2} = -\frac{13.6\ \text{eV}}{n^2}$
- $E_1 = -13.6\ \text{eV}$ (ground state)
- $E_\infty = 0$ (ionization)
Typical Problem Parts
- (a) State Bohr's postulates
- (b) Derive expression for orbital radius $r_n$
- (c) Calculate $r_n$ for a given $n$, or find $n$ for a given radius
- (d) Calculate energy of photon emitted during transition $n_i \to n_f$
Common Exam Variations
- Hydrogen-like ions ($Z > 1$): $r_n = \dfrac{n^2 a_0}{Z}$, $E_n = -\dfrac{Z^2 \cdot 13.6\ \text{eV}}{n^2}$
- Velocity in nth orbit: $v_n = \dfrac{Z e^2}{2\epsilon_0 n h} = \dfrac{Z \alpha c}{n}$ where $\alpha \approx 1/137$ (fine structure constant)

C6: Photoelectric Effect

Leak keywords: Review past 3 years

Detailed Prep Notes

Core Equations (Must Memorise)
- Photon energy: $E = hf = \dfrac{hc}{\lambda}$
- Einstein's photoelectric equation: $K_{\text{max}} = hf - \phi$
- Work function: $\phi = hf_0$ where $f_0$ = threshold frequency
- Threshold frequency: $f_0 = \phi/h$
- Cutoff wavelength: $\lambda_c = hc/\phi$
- Stopping potential: $eV_s = K_{\text{max}} = hf - \phi$
- $V_s = \dfrac{h}{e}f - \dfrac{\phi}{e}$ (linear: slope = $h/e$, intercept = $-\phi/e$)
- Maximum speed: $v_{\text{max}} = \sqrt{2K_{\text{max}}/m_e}$
Graph Interpretation (Common Past Year)
- $K_{\text{max}}$ vs $f$: straight line with slope $h$, y-intercept = $-\phi$, x-intercept = $f_0$
- $V_s$ vs $f$: straight line with slope $h/e$, y-intercept = $-\phi/e$
- Photocurrent vs $V$: saturation current at large positive $V$, cutoff at $V = -V_s$
Key Experimental Observations
- No time lag: emission is instantaneous when $f > f_0$
- $K_{\text{max}}$ depends on $f$, not on intensity
- Photocurrent depends on intensity, not on $f$ (for $f > f_0$)
- Below threshold frequency, no emission regardless of intensity
Typical Past Year Question Structure (Repeat pattern)
- (a) Define work function, threshold frequency
- (b) Calculate photon energy given $\lambda$ or $f$
- (c) Find $K_{\text{max}}$ given $\phi$ and photon energy
- (d) Calculate stopping potential $V_s$
- (e) Find $v_{\text{max}}$ of ejected electrons
- (f) Explain: what happens if intensity is doubled? What happens if frequency is increased?
- (g) Graph question: draw $K_{\text{max}}$ vs $f$, label slope and intercepts
Useful Constants
- $h = 6.63 \times 10^{-34}\ \text{J·s}$
- $c = 3.00 \times 10^8\ \text{m/s}$
- $e = 1.60 \times 10^{-19}\ \text{C}$
- $m_e = 9.11 \times 10^{-31}\ \text{kg}$
- $hc = 1240\ \text{eV·nm}$ (very useful for wavelength problems)
- $1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$
Review Past 3 Years' Questions
- Common themes to look for:
  - Multi-part calculation from wavelength → energy → $K_{\text{max}}$ → $V_s$ → $v_{\text{max}}$
  - Comparison of different metals (different $\phi$ values)
  - Dual nature: explaining why the particle model (photon) explains what wave theory cannot
  - If past papers include Millikan's experiment / experimental setup, review those too

Which 4 Questions to Choose in Section C

Question	Topic	Difficulty	Recommended For	Strategy
C1	Magnetism — Gauss & Ampere Derivation	Medium-Hard	Everyone	Derivation is predictable from past years. 4-wire problems are systematic. "Sphere" hint suggests Gauss's law for magnetism. Strong pick.
C2	EM — AC Motor Torque	Medium	Those comfortable with $\tau = \mu \times B$	Formula-driven, derivation-heavy. Pick if you like magnetism.
C3	Transformer — Self & Mutual Induction	Medium	Everyone	Well-defined formulas, derivation of solenoid $L$, transformer ratios. Strong pick.
C4	Semiconductor & Biasing	Medium	Everyone	Very detailed leak — you know exactly what will be asked (clipper, voltage divider stability, comparison, $I_B$ calc, beta independence). Strongest pick — do NOT skip.
C5	Atomic — Radius Derivation	Medium	Everyone	Bohr radius derivation is standard from any textbook. Strong pick.
C6	Photoelectric Effect	Hard	Those who practised past years	Requires recall of past 3 years questions. Unpredictable. Only pick if you've reviewed thoroughly.

[!tip] Recommended Selection: C4 + C3 + C5 + C1 These four have the most predictable content from the leak. C4 (Semi) has the most detailed leak info. C3 (Transformer) and C5 (Atomic) are standard derivations. C1 (Magnetism) is also standard but slightly harder. Avoid C6 unless you've done all past papers.

Section Selection Strategy Summary

Decision Flowchart

Start: Open exam, read ALL questions (3 min)
│
├─ Section B (pick 3 of 4)
│  ├─ Always pick: B1 (Electrostatic) + B2 (Capacitor+DC)
│  ├─ Then pick: B3 (AC Phasor) if comfortable with phasors
│  └─ Drop: B4 (Claims & RLC) unless AC is your strength
│
└─ Section C (pick 4 of 6)
   ├─ Always pick: C4 (Semi + Biasing) — most detailed leak!
   ├─ Always pick: C3 (Transformer) — standard derivation
   ├─ Always pick: C5 (Atomic Radius) — standard derivation
   ├─ Strongly consider: C1 (Magnetism) — predictable from past years
   ├─ Consider if confident: C2 (AC Motor Torque)
   └─ Consider if well-prepared: C6 (Photoelectric) — needs past year review

Time Allocation per Section

Section	Questions	Total Time	Per Question	Buffer
A	15 structured	30 min	~2 min	0 min
B	3 long Q	55 min	~18 min each	1 min
C	4 long Q	75 min	~18-19 min each	0 min
Total	22	160 min	—	—

[!warning] Time Management If stuck on a Section A question for >3 min, move on. For B & C, if a part takes >8 min, move to the next part and come back. Completing all selected questions beats perfect answers on some.

Key Formulas to Memorise (Cross-Section)

Electrostatics & Capacitance

Formula	Context
$\vec{F} = \dfrac{kQq}{r^2}\hat{r}$	Coulomb's law, vector form
$\vec{E} = \dfrac{kQ}{r^2}\hat{r}$	Electric field of point charge
$\vec{F} = q\vec{E}$	Force on charge in field
$a_y = qE/m$	Acceleration in uniform E-field
$C = \kappa\epsilon_0 A/d$	Parallel plate capacitance
$U = \frac12 CV^2 = Q^2/2C$	Energy stored

DC & AC Circuits

Formula	Context
$\tau = RC$	RC time constant
$q(t) = Q_0(1 - e^{-t/\tau})$	Charging capacitor
$q(t) = Q_0 e^{-t/\tau}$	Discharging capacitor
$X_L = \omega L$, $X_C = 1/\omega C$	Reactances
$Z = \sqrt{R^2 + (X_L - X_C)^2}$	RLC impedance
$\phi = \tan^{-1}((X_L-X_C)/R)$	Phase angle
$f_0 = 1/(2\pi\sqrt{LC})$	Resonance frequency

Power in AC

Formula	Context
$P_e = V_{\text{rms}}I_{\text{rms}}\cos\phi$	Real power
$P_{LC} = V_{\text{rms}}I_{\text{rms}}\sin\phi$ (inductive)	Inductive reactive power
$P_{CC} = V_{\text{rms}}I_{\text{rms}}\sin\phi$ (capacitive)	Capacitive reactive power
$P_A = V_{\text{rms}}I_{\text{rms}}$	Apparent power

Magnetism & Transformers

Formula	Context
$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$	Ampere's law
$B(r) = \mu_0 I r/(2\pi R^2)$, $r<R$	Inside wire
$B(r) = \mu_0 I/(2\pi r)$, $r>R$	Outside wire
$\vec{F}_B = q\vec{v} \times \vec{B}$	Lorentz force
$r = mv/qB$	Cyclotron radius
$\tau = NIAB\sin\theta$	Torque on loop
$L = \mu_0 N^2 A/l$	Solenoid inductance
$V_2/V_1 = N_2/N_1$	Transformer voltage ratio

Semiconductors

Formula	Context
$I_E = I_B + I_C$	Transistor KCL
$I_C = \beta I_B$	Current gain
$I_B = (V_{CC} - V_{BE})/R_B$	Fixed bias
$I_B = (V_{CC} - V_{BE})/(R_B + (\beta+1)R_E)$	Emitter-stabilized bias

Atomic & Photoelectric

Formula	Context
$r_n = 4\pi\epsilon_0 n^2\hbar^2/(m_e e^2) = n^2 a_0$	Bohr radius
$a_0 = 0.529\ \text{Å}$	Bohr radius (value)
$E_n = -13.6/n^2\ \text{eV}$	Energy levels
$K_{\text{max}} = hf - \phi$	Photoelectric effect
$eV_s = K_{\text{max}}$	Stopping potential

Quick Pre-Exam Checklist

[ ] Section A: Practised RC transient, op-amp formula recall, Ampere's law inside/outside wire
[ ] Section B: Know B1 (vector E + projectile), B2 (dielectric + voltage divider), B3 (phasor + power triangle)
[ ] Section C: Prepared C4 (biasing, voltage divider stability, $I_E = I_B + I_C$, beta independence), C3 (transformer ratios, self/mutual inductance derivation), C5 (Bohr radius derivation), C1 (Gauss & Ampere derivation, 4-wire systems)
[ ] Formulas: All key formulas memorised (see above)
[ ] Constants: $k$, $\epsilon_0$, $h$, $c$, $e$, $m_e$, $hc = 1240\ \text{eV·nm}$ committed to memory
[ ] Past Years: Reviewed past 3 years for photoelectric effect (C6)
[ ] Equipment: Calculator (charge batteries!), ruler for phasor diagrams, pencil for circuit sketches
[ ] Lenz Law: ⚠️ DO NOT STUDY for Section A (confirmed not tested)

Related Resources

FAD1022 Exam Focus — Leak Topics — Complementary topic-content page
FAD1022 - Basic Physics II — Course main page
FAD1022 Mastery Set — Interleaved Physics II — Interleaved problem set
FAD1022 Rapid-Fire Drill Pack — CQ2 Capacitor & DC
FAD1022 Rapid-Fire Drill Pack — CQ3 AC Analysis
FAD1022 Rapid-Fire Drill Pack — CQ4 Magnetism
FAD1022 Rapid-Fire Drill Pack — CQ7 Atomic Physics

Formula Sheets

[!info] Revision Note This page was created from leaked exam structure information dated 2026-05-02. The leak specifies exact question breakdowns, marks, and topics for Sections A, B, and C. Use as a structural guide for time management and question selection strategy.