System Engineers’ tip to HKCEE/HKALE Math and Physics

Shortly after I’ve graduated with Mathematics and Electrical (and Computer) Engineering degrees, I realized a few supposedly difficult topics in Hong Kong’s Mathematics and Physics (Electric Circuits) curriculum was taught in unnecessarily painful ways.

Here’s an article I’ve written to show that it is less work to teach secondary (high) school students a few easy-to-learn university math topics first than teaching them dumb and clumsy derivations/approaches to avoid the pre-requisitesHKDSE EE Tips

Here are the outline of the article

• Complex numbers with Euler Formula
• Trigonometric identities can be derived effortlessly using complex number than tricky geometric proofs
• Inverting matrices using Gaussian elimination instead of messing with cofactors and determinants
• Proper concepts of circuit analysis and shortcuts
• Solving AC circuits in a breeze with complex numbers instead of remembering stupid rules like ELI and ICE rules and messy trigonometric identities.

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變幻才是永恆 = 世界是線性?

– Sep 17, 2005

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喼神 Paul Ho (God of Briefcase) PAUL HO's unHOLY QUOTATIONs

PAUL HO’s unHOLY QUOTATIONs (All in Chinglish/English because SPC is an EMI school)

• Open the door and see the mountain (翻譯: 開門見山)
• There is a Chinese saying … (翻譯: 俗語有話…)
• Don’t put your hands under your desk. People might think you are playing some toys.
People might think that you are having a lucky draw.
People might think that you are playing some toys.
• Fishing Club (上堂釣魚/こっくり)
• Mr. Tso, a poet who can make a poem in seven steps (翻譯: 七步成詩)
• ICAC might stand for “I Can Accept Cash” (When he taught EPA)
• The term “tertiary industry” (三級工業) might have a better Chinese translation…
• ICAC might stand for “Ice-Cream And Coca-cola”
• ICAC might meant “I Can Accept Cheques”
(I overused his “I can accept cash” in his Econ class, so he changed it to checks)
• Good Family Education (有家教)
• If someone is not happy with you, they’ll say hello to your family(問候你全家).
• If you use credit card in King Fu, they might say hello to your family(問候你全家).
• People don’t cry until they see the coffin (翻譯: 唔見棺材, 唔流眼淚)
• Lots of St Pauls boys go to HKU……………………….for lunch
• Kill the monkey to warn the chicken (殺雞警猴)

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The most important invariants in basic electronics

The two basic laws in circuit analysis, Kirchhoffs Voltage and Current Laws,

1. [KVL] Voltage across the same pair of points is the same no matter what paths you take
2. [KCL] Current stay the same along the same path

are often taught in basic circuit analysis, but most of the time, they taught it in the context of nodal analysis, which you have a little more complicated meshes with multiple theoretical power source (voltage or current) that simple series/parallel circuit rules are not enough to solve the puzzle.

However, these two fundamental concepts are useful to develop insights that help you estimate quantities in a circuit quickly like a pro.

Kirchhoffs Voltage Law [KVL] can be applied to a parallel circuit of 2 branches (often the case when measuring additional loading effect). Let say the two branches are applied (loaded) at a voltage output , which might change depending on the branches (loading).

You can exploit the algebra to quickly calculate the current of any branch without first computing the overall resistance or current:

Kirchhoffs Current Law [KCL] is useful in analyzing energy loss over resistance in wires . For example, in high school physics, we discuss why we have high voltage power lines for bulk energy transmission despite it’s more dangerous. The traditional explanation is

so the lower the current is (which can be done through stepping up the voltage, traditionally done with AC signal through transformers, to maintain the same power). But how about other form

Technically, it’s possible, but you have to be very careful that the voltage we are talking about is across the wire with resistive losses , NOT the load voltage .

changes depending on the output load , so you have to derive the assuming an arbitrary , which will happen to cancel itself out and end up the same as if you think of everything in terms of current first:

So the bottom line is that most of the time, it is easier to think in terms of current in most circuit analysis because current won’t change along the same path. This is especially true when your problem has varying impedances/load which will disturb the voltage.

Of course, if the problem screams direct application using KVL, don’t go all the way converting it back to current. You will find the current-first approach useful when we get to semiconductors like diode, voltage references, BJTs,.

I usually think of voltage as a consequence or effect of current flushing into a transducer (e.g. resistor), so it’s subjected to change and therefore messy to use when solving circuit puzzles. Solving circuit analysis problems are often an exercise of identifying invariants and inferring the remaining quantities.

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