Schedule

Chapter 3 · CLO1 · Weeks 3–4

Simple Resistive Circuits

Chapter 3 turns the laws of Chapter 2 into shortcuts. Instead of writing a KCL or KVL equation for every node and loop, you will combine resistors, split a voltage or a current in one line, and handle networks that look impossible at first sight. Most circuits in this course, and most of the midterm, use these shortcuts.

When

  • Week 3 · Tue 20 Oct, Thu 22 OctResistors in series and in parallel. Voltage and current division.
  • Week 4 · Tue 27 Oct, Thu 29 OctDelta-to-wye equivalent circuits. Problems.

Quiz Device-free quiz at the start of week 5, session 1 (Tue 3 Nov)

Materials

Open practice · AI allowedSolve the practice sheet onlineEach question tells you at once whether your answer, and your reason, are right.Start the sheet

What you will learn

  • Series resistors: they carry the same current, and their resistances add.
  • Parallel resistors: they share the same two nodes and the same voltage. For two of them, the equivalent is the product over the sum, $R_1R_2/(R_1 + R_2)$.
  • Voltage division: in a series string, each resistor takes a share of the voltage in proportion to its resistance.
  • Current division: in a parallel group, each resistor takes a share of the current in inverse proportion to its resistance.
  • Loading: connecting a load to a voltage divider changes its output, unless the load is much larger than the resistor it sits across.
  • Delta-to-wye (Δ-to-Y) and wye-to-delta (Y-to-Δ): the tool for bridges and other networks with no series or parallel pairs.

Later in this course

ChapterWhere Chapter 3 comes back
4 Analysis techniquesThévenin and Norton equivalents, source transformations and maximum power transfer all need $R_{eq}$; dividers are the quickest way to check a node voltage
5 Operational amplifiersThe gain of an inverting or non-inverting amplifier is set by a ratio of two resistors; in the non-inverting amplifier they form a voltage divider
6 Inductors and capacitorsInductors combine like resistors; capacitors combine the other way round
7 First-order circuitsThe time constant $\tau = RC$ or $L/R$ uses the equivalent resistance seen by the capacitor or inductor

In your program

  • Electrical and Electronics: a transistor amplifier is biased with a voltage divider, and every sensor input is a divider whose loading must be checked.
  • Computer, Communication and Telecom: pull-up resistors and level shifters are voltage dividers, and sensors are often connected to a microcontroller’s analog input through one.
  • Biomedical: strain gauges and many pressure sensors sit in a Wheatstone bridge, the circuit you will analyse in S12 and S13.
  • Mechanical and Industrial: a heater with two elements gives low, medium and high settings by connecting them in series, alone or in parallel.
  • Surveying: the level sensors in many instruments are read through a bridge or a divider, so their output depends on the same ratios.

As an engineer

  • One line instead of four equations. A divider gives a voltage or a current in one step, and it tells you at a glance how the answer changes when a resistor changes.
  • Loading is a design rule. A divider only delivers its design voltage if the load is much larger than the bottom resistor (S4, S6, and Nilsson Example 3.4).
  • Bridges measure. When a bridge is balanced, no current flows across the middle; that is how a Wheatstone bridge measures an unknown resistance precisely (S13).

In real life

  • Your generator cable. A neighbourhood generator may hold 220 V at its terminals, but the cable to your home has resistance. The cable and your appliances form a voltage divider, so your home receives less than 220 V, and more so when you draw more current (S15).
  • A resistive touch screen. Screens of this kind, still used on some card terminals and industrial panels, find your finger with one voltage measurement per direction: the touch splits a resistive sheet into two parts, and the measured voltage is a fraction of the supply set by where you touch (S16, and Nilsson’s Practical Perspective for this chapter).

How to study this chapter, and where AI fits

  • AI tools are allowed on the practice sheet. Use them to check your work, not to replace it.
  • In a 2025 study of Gemini 2.5 Pro on undergraduate circuit problems, misread source polarities caused about a third of its wrong answers, and misread current directions nearly as many (arXiv 2512.10159). In this chapter, the commonest slips are putting the wrong resistance in a divider formula and treating two resistors as series or parallel when they are not. S9 shows one: find it before you trust any answer.
  • Check every answer yourself: resistors in parallel must have the same voltage, a divided voltage or current can never be larger than the total, and the powers must add to zero. These checks need no device.
  • The quiz is device-free, and every question is a twin of a practice-sheet question. If you can do the sheet on your own, you will do well on the quiz.

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