Linear and Non-linear Circuits

Basic Electrical & Electronics Engineering — Basic Concept, NEC licence examination syllabus (Nepal Engineering Council).

Linear and Non-linear Circuits: when Ohm's law stops applying

A filament lamp is not a resistor, and that distinction matters.

Plot voltage against current for a carbon resistor and you get a straight line through the origin. Do the same for a filament bulb and the line bends. For a diode it barely moves and then shoots up. All three are passing current — but only the first obeys Ohm's law, and only the first can be analysed with the techniques from the previous topics.

The defining test

A circuit/element is LINEAR if its V–I graph is a straight line through the origin — meaning R is CONSTANT, independent of the voltage or current applied. Linear elements obey: · Superposition (responses add) · Homogeneity (double the input → double the output) If either fails, the element is NON-LINEAR.

⚔️ Linear vs Non-linear

LinearStraight-line V–I through origin. Constant R. Obeys Ohm's law and superposition. Examples: carbon resistor, ideal inductor, ideal capacitor.

Non-linearCurved V–I. R changes with operating point. Superposition fails. Examples: semiconductor diode, BJT, filament lamp, thermistor, iron-cored inductor (saturation).

Why it mattersEvery theorem in Section 2 — superposition, Thevenin, Norton — is only valid for linear circuits. That is the real reason this distinction is in the syllabus.

The filament lamp is the classic exam example because it looks like a resistor but isn't: as current rises the tungsten heats up, its resistivity increases, and R climbs. A cold 100 W bulb might measure 30 Ω, but operate at 480 Ω. That is a 16× difference. It also explains why bulbs usually blow at the moment you switch them on: while the filament is still cold its resistance is low, so a large inrush current flows for a brief moment.

Worked example — testing linearity

An element gives I = 2 A at V = 4 V, and I = 3 A at V = 9 V. Is it linear?

At point 1: R = V/I = 4/2 = 2 Ω At point 2: R = V/I = 9/3 = 3 Ω R is not constant → NON-LINEAR. Homogeneity check: doubling V from 4 to 8 should double I from 2 to 4 if linear. Interpolating the data, it doesn't. Confirmed non-linear.

💡 Exam angle: usually a 2–4 mark definition-with-examples question. Answer it in three parts: state the straight-line-through-origin test, give two examples each side, and add the consequence — that network theorems only apply to linear circuits. That last point is what separates a full-mark answer from a half one.

Syllabus points

Difference with examples

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