Applying the PSC
- An element has v = 6 V with the current arrow of i = 2 A entering its + terminal.
- Labels match the PSC, so p = v·i = 12 W.
- Positive → the element absorbs 12 W.
← CA-1 · CHARGE, CURRENT & VOLTAGE
Sources and sign conventions
YOU WILL BE ABLE TO
- State the passive sign convention (PSC) and apply it without hesitation.
- Determine from a computed power whether an element absorbs or delivers.
- Describe ideal independent voltage and current sources.
- Recognise dependent sources and why they matter later.
Circuit analysis produces signed numbers, and the signs only mean something if everyone labels things the same way. The agreement is the passive sign convention, and it is worth memorising word-for-word.
That's the whole convention. Every sign headache in this course reduces to applying it carefully. Note what it does not say: it does not say current "really" flows into the + terminal — it says if your labels are drawn that way, then p = v·i means absorption. Labels are your choice; the convention just makes the arithmetic honest.
Now, the elements that push charge around. An ideal independent voltage source maintains a fixed voltage across its terminals no matter what current flows through it — a perfect 3.3 V rail stays at 3.3 V whether it supplies 1 mA or 1 A. An ideal independent current source forces a fixed current through itself no matter what voltage appears across it. Real sources are neither (a battery's voltage sags under load), but the ideal models are accurate enough to design with, and CA-4 shows how to model the sag with a Thevenin resistance.
A dependent (controlled) source is one whose value is set by a voltage or current elsewhere in the circuit — for example, a source whose output is 50 times some other branch's current. These look artificial now, but they are how transistors and op-amps are modelled: an entire amplifier is, at its core, a dependent source. You'll meet all four flavours (VCVS, VCCS, CCVS, CCCS) properly in CA-3 and then constantly in Microelectronics.
One warning about ideal sources: never place two ideal voltage sources of different values in parallel, or two different ideal current sources in series — the definitions contradict each other and the model breaks. Real circuits resolve the conflict by violence (smoke); the maths resolves it by refusing to have a solution.
Arrow enters the − terminal
- An element has v = 6 V but the 2 A arrow enters its − terminal.
- Labels are anti-PSC, so p = −v·i = −12 W absorbed.
- Negative absorption → the element delivers 12 W. (It's behaving as a source.)
A battery being charged
- A 12 V battery is connected to a charger pushing 3 A into its + terminal.
- Current enters the + terminal: PSC applies directly. p = 12 × 3 = +36 W.
- The battery is absorbing 36 W — correct, it's being charged. The same battery discharging would have current leaving its + terminal and p would come out negative: delivering.
PRACTICE
An element has v = 4 V and i = −3 A, with the current arrow entering the + terminal. Absorbing or delivering, and how much?
A 3.3 V rail supplies 150 mA to a sensor board (current leaves the rail's + terminal). Compute the rail's absorbed power under the PSC and interpret it.
Why is connecting a 5 V ideal source in parallel with a 3.3 V ideal source contradictory?
A circuit contains a 9 V source delivering 1.8 W and two other elements. One absorbs 1.2 W. What does the other absorb, and what current does the source supply?