Exam Frequency Analysis

5 years of ELE202 exams analyzed. Every concept ranked by frequency with weighted priority scoring.

W21 Winter 2021 W22 Winter 2022 P23 Spring 2023 P24 Spring 2024 W25 Winter 2025 (×1.5 weight)

S Guaranteed Questions — 100% Frequency

These five concepts appear in every single exam and account for 100 marks total. Master these first.

Core Concepts

  1. First-Order Transients (RL/RC) — Q1, ~20 marks
  2. Nodal Analysis — Q2/3, ~20 marks
  3. Mesh Analysis — Q2/3, ~20 marks
  4. Thevenin Equivalent — Q4, ~20 marks
  5. Power Calculations — Q5/6, ~20 marks

Weighted Priority

Weighted Score5.4/5.0
Exams Tested5/5 (100%)
Total Marks~100 per exam

A High Frequency — 80%

Source Transformation Method

⚠ Required Method

Using other methods when Source Transformation is specified results in ZERO marks, even if your answer is mathematically correct.

ExamQuestionPurposeMarks
W25Q4(i)Finding Vth8
P24Q4(1)Finding Vth8
W22Q4(1)Finding Vth8
W21Q4(1)Finding Vth8

Superposition Principle

Required for initial/final conditions when multiple sources are present. Used in 4/5 exams.

B Medium Frequency — 60%

Maximum Power Transfer

For maximum power: $$Z_L = Z_{th}^*$$ (complex conjugate)

Maximum power: $$P_{max} = \frac{|V_{th}|^2}{4 \cdot \text{Re}(Z_{th})}$$

Cramer's Rule

Explicitly required in W22, W21, P23 for solving matrix systems. 2 marks per application.

C Standard — 40%

  • Phasor Diagrams
  • Time-Domain Conversion

D Single Occurrence — 20%

  • Dependent Sources (W21)
  • Student Number Values (W21)

Required Methods Summary

Method Exam Question Weight
Source TransformationW25Q4(i)8 marks
P24Q4(1)8 marks
W22Q4(1)8 marks
W21Q4(1)8 marks
SuperpositionP23Q1A(a)5 marks
P23Q2(a)9 marks
W22Q1b(i)4 marks

Concept Workbook

Deep explanations of every tested concept. Circuit diagrams, formulas, and systematic solution processes.

S 1. First-Order RL Transients

First-order circuits contain one energy storage element. When a switch changes state, energy transfers between the storage element and resistors over time.

Universal Transient Equation
$$i_L(t) = i_L(\infty) + [i_L(0^+) - i_L(\infty)]e^{-t/\tau}$$

Basic RL Circuit

Vs R t=0 L

Key Principles

  • Inductor at DC steady state (t → ∞): Acts as short circuit (wire)
  • Inductor at t = 0+: Acts as current source with value iL(0+)
  • Current Continuity: $$i_L(0^+) = i_L(0^-)$$ — current cannot change instantaneously
  • Time Constant: $$\tau = \frac{L}{R_{th}}$$ where Rth is the Thevenin resistance seen by the inductor

6-Step Solution Process

Find iL(0−) — Before Switch Action ▼

Circuit state: Steady state, switch in original position

Inductor: Replace with SHORT CIRCUIT (wire)

Calculate current through inductor using DC analysis.

Find iL(0+) — Immediately After Switch ▼

Apply current continuity principle:

$$i_L(0^+) = i_L(0^-)$$

This is your initial condition.

Find iL(∞) — New Steady State ▼

Circuit state: Switch in new position, steady state reached

Inductor: Again a SHORT CIRCUIT

Method: Use SUPERPOSITION if multiple sources present

Find τ — Time Constant ▼

Deactivate all sources, find Rth looking into inductor terminals:

$$\tau = \frac{L}{R_{th}}$$
Write iL(t) Expression ▼
$$i_L(t) = i_L(\infty) + [i_L(0^+) - i_L(\infty)]e^{-t/\tau} \quad \text{for } t > 0$$
Find vL(t) if Required ▼
$$v_L(t) = L\frac{di_L}{dt} = R_{th}[i_L(0^+) - i_L(\infty)]e^{-t/\tau}$$

S 2. First-Order RC Transients

Universal Transient Equation
$$v_C(t) = v_C(\infty) + [v_C(0^+) - v_C(\infty)]e^{-t/\tau}$$

Basic RC Circuit

Vs R t=0 C

Key Differences from RL

PropertyRL CircuitRC Circuit
Time Constant$\tau = L/R$$\tau = RC$
Continuity$i_L(0^+) = i_L(0^-)$$v_C(0^+) = v_C(0^-)$
Steady StateL = Short CircuitC = Open Circuit
At t = 0+Current sourceVoltage source

S 3. Nodal Analysis (AC Phasor)

Nodal analysis uses KCL at each non-reference node. Sum of currents entering = sum of currents leaving.

V̄s1 Z1 V̄1 Z3 V̄2 Īs Z2

Process

  1. Convert to phasor: $v(t) = V_m \cos(\omega t + \phi) \rightarrow \bar{V} = V_m \angle \phi$
  2. Identify non-reference nodes: $\bar{V}_1, \bar{V}_2, \ldots$
  3. Write KCL at each node
  4. Express currents as $(\bar{V}_{node} - \bar{V}_{adjacent})/Z$
  5. Form matrix and solve
Impedances
$$Z_R = R \quad \quad Z_L = j\omega L \quad \quad Z_C = \frac{1}{j\omega C} = \frac{-j}{\omega C}$$

S 4. Mesh Analysis (AC Phasor)

Mesh analysis uses KVL around each mesh (loop without other loops inside).

V̄s1 Z1 Z3 Z2 V̄s2 Ī1 ↷ ↶ Ī2

Key Points

  • Assign clockwise mesh currents: $\bar{I}_1, \bar{I}_2$
  • Shared elements: $(\bar{I}_1 - \bar{I}_2) \times Z$
  • Write KVL summing voltages around each mesh

S 5. Thevenin Equivalent

Any linear circuit can be reduced to a voltage source $\bar{V}_{th}$ in series with impedance $\bar{Z}_{th}$.

⚠ Required in 4/5 Exams

Source Transformation is the required method for finding $V_{th}$. Other methods = 0 marks.

Source Transformation

Vs Z Transform I = V/Z Is Z
Voltage → Current
$$I = \frac{V_s}{Z}$$
Current → Voltage
$$V = I_s \times Z$$

S 6. Power Calculations

Power Triangle

P (Real) Q (Reactive) |S| (Apparent) θ
QuantityFormulaUnit
Complex Power$\bar{S} = \bar{V} \times \bar{I}^* = P + jQ$VA
Apparent Power$|S| = |V| \times |I|$VA
Real Power$P = |S| \times PF = I^2R$W
Reactive Power$Q = I^2X$VAR
Power Factor$PF = \cos(\theta) = P/|S|$—
PF Sign Convention

Lagging PF (inductive): Q > 0, θ > 0

Leading PF (capacitive): Q < 0, θ < 0

B 7. Maximum Power Transfer

Maximum Power Condition
$$Z_L = Z_{th}^* \quad \text{(complex conjugate)}$$ $$P_{max} = \frac{|V_{th}|^2}{4 \cdot \text{Re}(Z_{th})}$$

Full Worked Solutions

Every question type solved step-by-step with redrawn circuits at each stage.

S RL Transient with Superposition (W25 Style)

Problem

Switch open for long time. At t=0, closes. Find $i_L(t)$ using SUPERPOSITION.

V R1 t=0 R2 Is L
Find $i_L(0^-)$ — Before Switch Closes ▼

Circuit for t < 0: Switch OPEN, inductor = SHORT CIRCUIT (steady state)

V = 24V R₁ = 12Ω OPEN R₂ Iₛ (open) L → SHORT i_L(0-) = 2A

Analysis: Only V source is active. The current source is disconnected by the open switch.

$$i_L(0^-) = \frac{V}{R_1} = \frac{24\text{ V}}{12\ \Omega} = 2\text{ A}$$
Find $i_L(0^+)$ — Current Continuity ▼

At t = 0+: The inductor acts as a CURRENT SOURCE with value $i_L(0^-)$

V R₁ CLOSED R₂ Iₛ 2A = i_L(0+) L → I source
$$i_L(0^+) = i_L(0^-) = 2\text{ A}$$
Find $i_L(\infty)$ — Using SUPERPOSITION ▼

At t → ∞, switch is closed, inductor becomes SHORT CIRCUIT again.

Superposition: Analyze each source separately, then sum.

Due to V source alone (Iₛ → OPEN):
V R₁ SHORT Iₛ → OPEN i'_L = V/R₁ = 2A
$$i_L' = \frac{V}{R_1} = 2\text{ A}$$
Due to Iₛ alone (V → SHORT):
V→SHORT R₁ L = SHORT R₂ Iₛ = 4A All 4A flows through short (L)
$$i_L'' = I_s = 4\text{ A}$$
Total:
$$i_L(\infty) = i_L' + i_L'' = 2 + 4 = 6\text{ A}$$
Find τ — Time Constant ▼

Deactivate all sources to find $R_{th}$ seen by inductor:

V → SHORT, Iₛ → OPEN

V→SHORT R₁ = 12Ω R₂ = 6Ω Iₛ → OPEN L terminals R_th = R₁ || R₂ = 12Ω || 6Ω = 4Ω
$$R_{th} = R_1 \| R_2 = 12\ \Omega \| 6\ \Omega = 4\ \Omega$$ $$\tau = \frac{L}{R_{th}} = \frac{0.5\text{ H}}{4\ \Omega} = 0.125\text{ s}$$
Write $i_L(t)$ ▼
$$i_L(t) = 6 + (2 - 6)e^{-t/0.125} = 6 - 4e^{-8t}\text{ A}$$
Find $v_L(t)$ ▼
$$v_L(t) = L\frac{di_L}{dt} = 0.5 \times 32e^{-8t} = 16e^{-8t}\text{ V}$$

S Power Calculation — Find Z from Power Data

Given:

Apparent power $|S| = 500$ VA, PF $= 0.8$ leading, voltage $V = 100\angle 0°$ V at 60 Hz.

Find impedance Z and L or C value.

Find Current Magnitude ▼
$$|I| = \frac{|S|}{|V|} = \frac{500}{100} = 5\text{ A}$$
Find Impedance Magnitude ▼
$$|Z| = \frac{|V|}{|I|} = \frac{100}{5} = 20\ \Omega$$
Find Impedance Angle ▼
$$\theta = \cos^{-1}(PF) = \cos^{-1}(0.8) = 36.87°$$

Leading PF → capacitive: $\theta = -36.87°$

Write Impedance ▼
$$Z = 20\angle{-36.87°} = 20(0.8 - j0.6) = 16 - j12\ \Omega$$
Find C Value ▼
$$X_C = 12\ \Omega, \quad \omega = 2\pi \times 60 = 377\text{ rad/s}$$ $$C = \frac{1}{\omega X_C} = \frac{1}{377 \times 12} = 221\ \mu\text{F}$$

Answer: 16 Ω resistor in series with 221 μF capacitor

2-Day Intensive Study Plan

14-16 hours structured for maximum retention. Master all 5 exams independently.

Day 1: Transients + Analysis (8 hrs) Day 2: Power + Integration (8 hrs)

Day 1: Foundation & Core Concepts

09:00
Hour 1: RL Transient Fundamentals
  • Read 6-step process (15 min)
  • Memorize: $\tau = L/R$, $i_L(t)$ formula (10 min)
  • Practice one complete example (20 min)
10:00
Hour 2: RC Transient Fundamentals
  • Compare RL vs RC (10 min)
  • Memorize: $\tau = RC$, $v_C(t)$ formula (10 min)
  • Practice one complete example (20 min)
11:00
Hour 3: Superposition for Initial Conditions
⚠ Required in 4/5 Exams

Superposition is specified for $i_L(\infty)$ and $v_C(0^+)$ with multiple sources.

12:00
Hour 4: Transient Practice Problems
  • Solve RL problem (W25 style) — 20 min
  • Solve RC problem (P23 style) — 20 min
  • Self-assessment — 10 min
13:00
🍽 Lunch Break
14:00
Hour 5: Nodal Analysis
  1. Convert to phasor domain
  2. Write KCL at each node
  3. Form matrix, solve
15:00
Hour 6: Mesh Analysis
  1. Assign CLOCKWISE mesh currents
  2. Write KVL around each mesh
  3. Shared elements: $(I_1 - I_2) \times Z$
16:00
Hour 7: Thevenin with Source Transformation
⚠ 8 Marks at Risk

Other methods = 0 marks even if correct.

17:00
Hour 8: Analysis Practice
  • Nodal problem — 20 min
  • Mesh problem — 20 min
  • Thevenin problem — 15 min

Day 2: Power & Integration

09:00
Hour 1: Power Fundamentals
$$\bar{S} = P + jQ \quad |S| = |V||I| \quad PF = \frac{P}{|S|}$$
10:00
Hour 2: Find Z from Power
  1. $|I| = |S|/|V|$
  2. $|Z| = |V|^2/|S|$
  3. $\theta = \cos^{-1}(PF)$ (+lagging, -leading)
  4. $Z = |Z|\angle\theta$
  5. $L = X/\omega$ or $C = 1/(\omega|X|)$
11:00
Hour 3: Maximum Power Transfer
$$Z_L = Z_{th}^* \quad P_{max} = \frac{|V_{th}|^2}{4R_{th}}$$

Formula Quick Reference

Transients

$\tau$ (RL)$L/R_{th}$
$\tau$ (RC)$R_{th} \times C$
$i_L(0^+)$$= i_L(0^-)$
$v_C(0^+)$$= v_C(0^-)$

Power

$\bar{S}$$P + jQ$
$|S|$$|V| \times |I|$
$P$$|S| \times PF$
$PF$$\cos(\theta)$

Impedance

$Z_R$$R$
$Z_L$$j\omega L$
$Z_C$$-j/(\omega C)$

Max Power

$Z_L$$Z_{th}^*$
$P_{max}$$|V_{th}|^2/(4R_{th})$

Exam Day Strategy

QTopicTimeKey Tip
1Transients35 minDraw t<0 and t>0 circuits
2Nodal35 minCheck matrix twice
3Mesh35 minClockwise currents!
4Thevenin35 minUse Source Transform
5Power35 minShow all values
🎯 Common Mistakes
  • Forgetting specified method (Superposition/Source Transform)
  • Wrong initial condition (check before vs after switch)
  • Wrong time constant formula ($L/R$ vs $RC$)
  • Wrong impedance sign ($+j$ vs $-j$)
  • Mixing lagging vs leading PF