ELECTENG291: nail every assessment, not just read the notes
Your complete guide to University of Auckland's fundamentals of electrical engineering course. See where the marks are, work real practice questions, and study with an AI tutor that knows ELECTENG291.
Sia generates ELECTENG291 practice questions, walks through node-voltage analysis and thevenin step by step, and quizzes you on the material the heaviest assessments weight most heavily.
Worked example
A series RC circuit with R = 2 kilohms and C = 10 microfarads is connected to a 10 V DC source at t = 0. The capacitor is initially uncharged. What is the capacitor voltage at t = 20 milliseconds?
Identify the circuit order and the time constant. This is a first-order RC circuit, so tau = RC = 2000 × 10e-6 = 0.02 seconds, that is 20 milliseconds.
Apply the general first-order solution: v(t) = v(final) + [v(0) − v(final)] × e^(-t/tau), which here gives v(t) = 10 − 10 × e^(-t/0.02).
Substitute t = 0.02 s, which is exactly one time constant. v = 10 × (1 − e^-1) = 10 × (1 − 0.3679) = 6.32 V. One time constant always brings a charging capacitor to about 63.2% of its final value.
The trap: Answering 3.68 V, which is 10 × e^-1. That is the decaying part of the response, not the capacitor voltage. It would be correct for a discharging capacitor starting at 10 V, or for the resistor voltage in this charging circuit. Always check whether the quantity you want is rising toward its final value or decaying from its initial one before applying the exponential. classic slip!
One exam decides 40% of your grade. Must sit the exam to be eligible for a passing grade, otherwise a Did Not Sit grade is recorded. This whole page is built around that.
Overview
What ELECTENG291 is, and where it sits
ELECTENG 291 is the University of Auckland's second-year circuits course and the bridge between knowing what a resistor does and being able to predict what an arbitrary network will do in the time, s and frequency domains. It follows ELECTENG 101 and carries a restriction against ELECTENG 202.
The course runs in three modules. The first establishes circuit classification and the analysis toolkit: signals and sources, linear versus non-linear behaviour, node-voltage analysis, superposition, and Thevenin and Norton equivalents. The second moves into transient behaviour, first and second-order circuits, differential equation modelling and the Laplace transform. The third covers AC steady state: phasors, impedance, power characterisation and frequency response.
The mathematical demand rises sharply at the Module 2 boundary. Up to that point you are solving networks algebraically; afterwards you are solving differential equations, transforming between domains, and manipulating complex numbers under restricted-calculator conditions. That transition is where students either consolidate or fall behind, and the pace does not slow to let them catch up.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is ELECTENG291 hard, and how much time does it take?
ELECTENG291 is manageable if you keep a weekly rhythm and treat the back half as the main event. The pattern is consistent: it starts gently and steepens, and the heaviest assessment is the part that separates grades.
The difficulty curve and the assessment weighting point the same way: the back half is harder and worth more. Front-loading effort there is the highest-return decision in the course.
Is this course for you
Who tends to do well, and who tends to struggle
You will likely do well if
- You are fluent with complex numbers in both rectangular and polar form and can convert between them quickly with a restricted calculator.
- You set boundary conditions carefully before solving any transient. Most transient errors are initial-condition errors, not integration errors.
- You build your A4 sheet around what the provided formula page does not give you: second-order damping cases, phasor conversions, power relationships and partial-fraction patterns.
- You work the past tests. The course provides eight past tests with full solutions across four years, which is an unusually complete practice set.
You may struggle if
- You arrive at Module 2 without solid ELECTENG 101 mechanics, since the pace assumes them and the revision assignment is only worth 2%.
- You treat the Laplace transform as a lookup table rather than a method, which fails as soon as initial conditions are non-zero.
- You skip tutorials because of the 7% cap. The cap forgives the marks, not the practice, and the tutorial topics map directly onto the exam.
- You leave AC power to the end. It is the last material taught and it reliably appears in assessment.
- Learn to recognise which domain makes a question easy. The same circuit is trivial in one domain and painful in another, and choosing well is the examinable judgement.
- Drill the three second-order damping cases until you can classify a circuit from its characteristic equation without hesitation.
- For AC power, keep real, reactive, apparent and complex power strictly distinct, and be able to compute power factor and correct it.
- Practise under exam conditions with only your A4 sheet and the provided formula page. Discovering that your sheet is missing something during the exam is the expensive way to find out.
Syllabus
The 12 topics, lecture block by lecture block
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Signals, sources and passive component behaviour
Module 1 notes, L01 to L04Course structure, signal types, independent and dependent sources, and how resistors, capacitors and inductors behave.
T2 · Linear versus non-linear circuits
Module 1 notes, L05 to L07Additivity and homogeneity as the test for linearity, and why it determines which methods are available.
T3 · Equivalent resistance and the load-line method
Module 1 notes, L08 to L09Series and parallel reduction, and the graphical load-line solution for non-linear elements.
T4 · Node-voltage analysis and superposition
Module 1 notes, L10 to L11Systematic nodal analysis, and decomposing a multi-source circuit one source at a time.
T5 · Thevenin and Norton equivalents
Module 1 notes, L12Reducing any linear two-terminal network to a source and a single impedance, and converting between the two forms.
T6 · First-order circuits and boundary conditions
Module 2 notes, L13 to L16RC and RL transients, the time constant, and establishing initial and final conditions correctly.
T7 · Second-order circuits
Module 2 notes, L17 to L19RLC transients, the characteristic equation, and overdamped, critically damped and underdamped responses.
T8 · The Laplace transform
Module 2 notes, L20 to L22Transform pairs, initial conditions carried into the transform, and the inverse by partial fractions.
T9 · Circuit analysis in the s-domain
Module 2 notes, L23 to L24Replacing components with s-domain impedances so that a differential equation becomes an algebraic one.
T10 · Sinusoidal signal representation
Module 3 notes, L25 to L27Trigonometric form, average and RMS values, and the complex exponential representation.
T11 · AC steady-state analysis with phasors
Module 3 notes, L28 to L31Reactance and impedance, phasor arithmetic, and phasor diagrams for series and parallel networks.
T12 · AC power, frequency response and three-phase systems
Module 3 notes, L32 to L34Instantaneous, average, reactive and apparent power, power factor and complex power; transfer functions and magnitude and phase response; balanced three-phase systems.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Final examination | 40% | Two-hour in-person exam of two equally weighted free-form questions. Restricted book and restricted calculator: one double-sided A4 sheet plus a provided formula page with Laplace pairs and the first-order general solution. Students are given 180 minutes for 120 minutes of material. University of Auckland Semester 1 examination period. Must sit the exam to be eligible for a passing grade, otherwise a Did Not Sit grade is recorded. |
| Tests | 24% | Two one-hour in-person restricted-book and restricted-calculator tests at 12% each. Mid-module checkpoints during the semester. Invigilated. |
| Online assignments | 15% | Three online assignments at 5% each. Across the semester. Individual submission. |
| Laboratories | 12% | Five laboratories, of which four are graded at 3% each. Lab 1 is a mandatory ungraded introduction to the instruments. Weeks 4, 6, 8 and 10. Lab 1 attendance is mandatory. |
| Tutorials | 7% | Eleven weekly tutorials at 1% each, capped at 7%, so four can be missed without penalty. Weekly from Week 2. Capped contribution. |
| Online revision assignment | 2% | A single revision assignment revisiting the ELECTENG 101 material the course assumes. Early semester. Individual submission. |
- You must attempt the final examination to be eligible for a passing grade. A student who does not sit receives a Did Not Sit grade. There is no separate component pass requirement.
- The exam is only two questions for 40% of the course, which means each is worth 20% and a topic you cannot attempt is unusually expensive. Time is generous at 180 minutes for 120 minutes of material, so the constraint is knowledge rather than speed. The provided formula page gives Laplace pairs and the first-order general solution, so your own A4 sheet should carry everything else.
This is a coursework course. Coursework carries 60% of the grade and the final examination is the single heaviest piece at 40%, so steady work across the semester decides your result more than any one sitting. Must sit the exam to be eligible for a passing grade, otherwise a Did Not Sit grade is recorded.
Final exam timing: During the University of Auckland Semester 1 examination period. Confirm the exact date and venue on your exam timetable.
How to actually pass it
A weekly rhythm, two checklists, and the traps to avoid
The course rewards consistency over cramming, and practice over re-reading. Here is the loop that works, then what to have nailed before each exam.
The weekly loop
Before the mid-semester checklist
- Reduce networks by series and parallel combination and find Thevenin and Norton equivalents reliably.
- Perform node-voltage analysis systematically, including circuits with dependent sources.
- Apply superposition correctly, deactivating sources the right way each time.
- Solve first-order RC and RL transients from boundary conditions using the general solution.
Before the final heaviest topics
- Classify and solve second-order circuits across overdamped, critically damped and underdamped cases.
- Move a circuit into the s-domain with initial conditions included, solve algebraically, and invert by partial fractions.
- Analyse AC steady-state networks with phasors and impedance, and draw the phasor diagram.
- Compute average, reactive, apparent and complex power, find the power factor, and handle a balanced three-phase system.
The mistakes that cost marks
Confusing the rising and decaying exponential. A charging capacitor reaches 63.2% of its final value in one time constant; the term 10 × e^-1 is the decaying part, not the capacitor voltage. Decide which quantity is rising and which is falling before substituting.
Getting boundary conditions wrong. Capacitor voltage and inductor current cannot change instantaneously. Establish those two continuously-valued quantities at the switching instant first, then derive everything else.
Dropping initial conditions in the Laplace transform. The transform of a derivative carries the initial value. Omitting it produces an algebraically clean but physically wrong answer, and it is a standard exam discriminator.
Mixing RMS and peak values in power calculations. AC power relationships assume RMS unless stated otherwise. Using peak values silently inflates every power result by a factor of two.
Teaching team
Who teaches ELECTENG291
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken ELECTENG291.
William Lee
Coordinates and lectures ELECTENG 291 in the Department of Electrical, Computer and Software Engineering, and runs the course office hours and exam preparation sessions.
Teaching team as listed in public course information. AskSia does not rate lecturers; star ratings are submitted by students who have taken ELECTENG291.
Formula & concept sheet
The vocabulary and formulas you must own
- Time constant
- For a first-order circuit, tau = RC or L/R. The response completes about 63.2% of its total change in one time constant and is essentially complete after five.
- First-order general solution
- v(t) = v(final) + [v(0) − v(final)] × e^(-t/tau), which covers both charging and discharging once the boundary values are set.
- Thevenin equivalent
- Any linear two-terminal network reduces to a single voltage source in series with a single impedance, seen from the terminals of interest.
- Superposition
- In a linear circuit the response to several independent sources equals the sum of the responses to each acting alone, with voltage sources shorted and current sources opened.
- Characteristic equation
- The polynomial in s whose roots determine a second-order circuit's natural response and classify it as overdamped, critically damped or underdamped.
- Damping classification
- Real distinct roots give an overdamped response, a repeated real root gives critically damped, and complex conjugate roots give an underdamped oscillatory response.
- Laplace transform
- An integral transform converting a differential equation in time into an algebraic equation in s, with initial conditions carried into the transformed expression.
- Impedance
- The complex ratio of phasor voltage to phasor current, combining resistance with reactance and holding both magnitude and phase information.
- Phasor
- A complex number encoding the amplitude and phase of a sinusoid at a fixed frequency, which turns differential relationships into algebraic ones.
- RMS value
- The equivalent DC value that would dissipate the same average power. For a sinusoid it is the peak divided by the square root of two.
- Power factor
- The cosine of the phase angle between voltage and current, equal to the ratio of real power to apparent power.
- Complex power
- S = P + jQ, combining real power P in watts with reactive power Q in volt-amperes reactive, with magnitude equal to apparent power.
Common acronyms: AC · DC · EMF · KCL · KVL · PF · RLC · RMS · VA · VAR.
Set texts
The prescribed reading
The syllabus references map straight onto these.
Fundamentals of Electric Circuits, any edition
Charles K. Alexander and Matthew N. O. Sadiku.
Where it fits
Prerequisites, related courses & why it matters
Prerequisite: ELECTENG 101. Restriction: ELECTENG 202. The course assumes fluency with the DC circuit analysis from ELECTENG 101, and includes an early online revision assignment to confirm it.
Your ELECTENG291 study toolkit
Study the course with Sia, not just read about it
Each tool already knows ELECTENG291: your syllabus, your texts, and where the marks are. Grouped by how you study, from first contact to exam week.
FAQ
Frequently asked questions
Is ELECTENG 291 hard?
It rates moderately hard. The concepts are standard second-year circuits material, but the mathematical demand is high: differential equations, Laplace transforms, complex arithmetic and phasors, all performed with a restricted calculator. Most of the difficulty is in Modules 2 and 3.
What can I take into the exam?
It is a restricted-book and restricted-calculator exam. You may bring one double-sided A4 cheat sheet. The course provides a formula page with Laplace transform pairs and the general solution for first-order circuits, so do not spend your own sheet on those.
Why is the exam only two questions?
The two-hour exam consists of two equally weighted free-form questions, each therefore worth 20% of the course. This makes topic coverage unusually important: there is nowhere to hide if one of the two lands on material you skipped.
Do I need to attend every tutorial?
There are eleven tutorials worth 1% each, capped at 7%. That means you can miss up to four without losing any marks. The tutorials are nonetheless the main structured practice in the course and the topics they cover map directly onto the tests and exam.
Is there a textbook?
None is prescribed. The course releases its own electronic notes per module on Canvas with lecture recordings on Panopto. Alexander and Sadiku's Fundamentals of Electric Circuits, any edition, is recommended as covering most but not all of the topics.
What happens if I do not sit the exam?
You receive a Did Not Sit grade and are not eligible for a passing grade regardless of your coursework marks. Sitting the exam is the one hard hurdle in this course.
Study ELECTENG291 with Sia
Work through node-voltage analysis, thevenin, first-order circuits and the rest of the course with a tutor that knows it and quizzes you on the topics the assessments weight most heavily.
Start studying with Sia
