ELECTENG291 · Fundamentals of Electrical Engineering
Circuit Fundamentals, Signals & Sources
Module 1 of University of Auckland ELECTENG 291 opens with the vocabulary every later chapter is written in: charge, current, voltage and power, the passive sign convention that fixes when power is absorbed or delivered, and the four ideal sources — independent and dependent voltage and current sources. Getting the sign convention automatic here is what keeps KVL and KCL signs correct in every solve that follows, and power/sign reasoning appears in the online Module 1 assignment, the in-person tests and the final exam.
What this chapter covers
- 01Charge, current i [A] and voltage v [V]; current as the flow of charge, voltage as energy per unit charge
- 02Instantaneous power p = v·i [W] and the passive sign convention (PSC): current into the + terminal → power absorbed = +vi
- 03Absorbing vs delivering power: p > 0 absorbs, p < 0 delivers; conservation of power around a circuit (ΣP = 0)
- 04Ideal independent sources: the voltage source (fixes v) and the current source (fixes i)
- 05Dependent (controlled) sources: voltage- or current-controlled voltage/current sources, set by another circuit variable
- 06Signal description x(t) = X + x̃(t): a DC/average component X plus a time-varying (AC) component x̃(t)
- 07Average value X = (1/T)∫_T x(t) dt over one period, the foundation for RMS and AC power later
Power and the passive sign convention
- +1State the convention. Under the passive sign convention the power absorbed by an element is p = +v·i when the reference current enters the '+' voltage terminal.
- +1Case (a): current enters the '+' terminal, so p = v·i = 12 × 2 = +24 W. Positive → the element absorbs 24 W (it is a load, e.g. a resistor).
- +1Case (b): the current now enters the '−' terminal, so in PSC the reference current is i = −2 A relative to the '+' terminal: p = v·i = 12 × (−2) = −24 W.
- +1Interpret the sign: p = −24 W means the element delivers 24 W to the rest of the circuit (it is acting as a source). Same magnitude, opposite role — set purely by which terminal the current enters.
Key terms
- Current (i)
- The rate of flow of electric charge past a point, i = dq/dt, measured in amperes [A]. A reference arrow fixes the assumed positive direction; a negative computed value just means the true flow is opposite the arrow.
- Voltage (v)
- The energy transferred per unit charge between two points, measured in volts [V], with a '+' and '−' reference polarity. Only differences of potential are physical, so a reference (ground) node is chosen.
- Instantaneous power (p)
- p(t) = v(t)·i(t) in watts [W]. Under the passive sign convention it is the power absorbed by the element; p > 0 means absorbing, p < 0 means delivering.
- Passive sign convention (PSC)
- The rule that the reference current is drawn into the element's '+' voltage terminal, so absorbed power is +vi. It is applied to every element and every terminal law (v = Ri, i = C dv/dt, v = L di/dt) in the course.
- Independent source
- An ideal element that fixes one variable regardless of the rest of the circuit: an independent voltage source sets its terminal voltage, an independent current source sets its current.
- Dependent (controlled) source
- A source whose value is set by another voltage or current in the circuit (e.g. a current source equal to 2·I0). Dependent sources model amplifiers and transistors and, unlike independent sources, are kept active when applying superposition.
Circuit Fundamentals, Signals & Sources FAQ
What is the passive sign convention and why does it matter?
It is the agreement that a reference current is drawn into the '+' voltage terminal of an element, so the power it absorbs is p = +vi. It matters because it makes every sign in the course consistent: the terminal laws v = Ri, i = C dv/dt and v = L di/dt are all written under it, and a single flipped current arrow reverses your KVL and KCL signs and can turn an absorbing element into a delivering one. Label the polarity and arrow first, every time.
How do I tell if an element absorbs or delivers power?
Compute p = vi under the passive sign convention. If p > 0 the element absorbs power (it behaves as a load); if p < 0 it delivers power (it behaves as a source). A resistor always absorbs; a source can do either depending on the circuit around it.
What is the difference between an independent and a dependent source?
An independent source fixes its voltage or current on its own, no matter what the rest of the circuit does. A dependent (controlled) source's value is set by some other circuit variable — for example a current source equal to 2·I0. This distinction is essential later: when you apply superposition you zero independent sources one at a time but always leave dependent sources active.
Can Sia help me with the basics in ELECTENG 291?
Yes, as a study aid. Sia can explain charge, current, voltage and power, drill the passive sign convention until absorbing-vs-delivering is automatic, and check the signs in your own worked attempts. It explains and quizzes; it does not complete graded assessment for you, and the University of Auckland's academic-integrity rules apply — confirm what is allowed on Canvas.
Exam move
Make the passive sign convention a reflex before you touch any numbers: on every element mark the '+'/'−' polarity and the assumed current arrow, then write p = vi and read the sign. Practise the absorbing-vs-delivering call on single elements until it is instant, because this is the habit that keeps KVL/KCL signs correct through Thévenin, transients and AC power. Learn the four source types and, in particular, what makes a dependent source different — it changes how you handle superposition and Thévenin resistance later. Finally, get comfortable splitting a signal into its DC average and time-varying parts, x(t) = X + x̃(t); the average X = (1/T)∫_T x dt is the seed for RMS and AC power in Module 3. Confirm assessment weightings on Canvas.
Working through Circuit Fundamentals, Signals & Sources in ELECTENG 291? Sia is AskSia’s AI Electrical Engineering tutor — ask any ELECTENG 291 Circuit Fundamentals, Signals & Sources question and get a clear, step-by-step explanation grounded in how ELECTENG 291 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
