diode models
The real diode curve is an exponential, which is awkward to do by hand. So engineers use models — deliberately simplified stand-ins that are 'wrong but useful'. Choosing a model is choosing how much accuracy you need versus how fast you want an answer, like using a road map versus a satellite photo.
Three models, from crudest to finest. (1) The ideal diode: a perfect one-way switch — zero volts when on, open when off. Good for getting the gist of which way current flows. (2) The constant-drop model: when on, a fixed 0.7 V (silicon); when off, open. This is the everyday workhorse for hand analysis. (3) The piecewise-linear model: a 0.7 V battery in series with a small resistance rs (the slope of the curve), so the drop grows a little with current — Vf = 0.7 V + I times rs. Beyond these, a SPICE model uses the full Shockley equation with real parameters.
The skill is matching model to question. Sketching a rectifier? The ideal or constant-drop model is plenty. Computing efficiency or heat in a 10 A supply? You need the piecewise resistance and the temperature drift. Designing something precise or fast? Drop to SPICE. A wrong answer usually comes not from a bad diode but from a model too crude for the job — or too fussy to finish.
A diode plus 100 ohm across 5 V. Ideal model: I = 5 / 100 = 50 mA. Constant-drop: I = (5 - 0.7) / 100 = 43 mA. Piecewise with rs = 10 ohm: I = (5 - 0.7) / (100 + 10) = 39 mA. Same circuit, three answers of rising honesty.
Pick the simplest diode model that still answers your question.
No model is 'the truth' — even SPICE is only as good as its parameters. The mistake beginners make is mixing precision (carrying 0.7000 V) with a model that is only good to a tenth of a volt.