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-requisites: HKDSE 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.
The two basic laws in circuit analysis, Kirchhoffs Voltage and Current Laws,
[KVL] Voltage across the same pair of points is the same no matter what paths you take
[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.