Circuit Variables

What you will learn

• Units and prefixes: reading 0.000047 A as 47 µA, and never mixing mA with A.
• Current and voltage: $i = dq/dt$ (charge per second) and $v = dw/dq$ (energy per coulomb).
• Power and energy: $p = vi$, and $w = \int p\,dt$.
• The passive sign convention: deciding from a diagram whether an element absorbs or delivers power.
• The power balance: the powers in any circuit add up to zero. This is your main self-check.

Later in this course

In your program

• Electrical and Electronics: every component has a power rating. At grid scale, the same sign rule decides which generator supplies and which load absorbs.
• Computer, Communication and Telecom: phones and sensors run on power budgets, and datasheets quote mW and µA on every page.
• Biomedical: medical devices are specified by energy and current. A defibrillator shock is set in joules, and patient leakage currents are limited in microamperes.
• Mechanical and Industrial: motors, pumps and electric vehicles are rated in kW, and plant energy audits are done in kWh.
• Surveying: field instruments and survey drones run on batteries rated in watt-hours.

As an engineer

• Units cost missions. In 1999 NASA lost the Mars Climate Orbiter because one team’s software reported thruster impulse in pound-force seconds while the navigation software expected newton-seconds (source).
• Signs carry meaning. Whether a battery is charging or discharging, or a solar inverter is feeding the grid or drawing from it, is the sign of $p$.
• Checking is the job. A power balance is how engineers verify an analysis before anything is built.

In real life

• Your generator subscription. In Lebanon, a private generator subscription is sized in amperes (5 A, 10 A, …) and billed per kWh at a tariff the Ministry of Energy and Water sets each month (source). The ampere size limits your power: 5 A × 220 V ≈ 1.1 kW at any moment, which is why the breaker trips when a kettle and a heater run together. The kWh meter counts your energy. Power versus energy is Chapter 1.
• Your power bank. A 10,000 mAh power bank at 3.7 V stores 37 Wh. Airlines allow up to 100 Wh in carry-on baggage, and 100–160 Wh only with airline approval (IATA).
• A car jump-start. Which car has the dead battery? The sign of $p$ tells you (booklet Problem 1.1).

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.
• AI chatbots often misread polarities and current directions in circuit diagrams. In a 2025 study of Gemini 2.5 Pro, misread source polarities caused about a third of its wrong answers on undergraduate circuit problems, and misread current directions nearly as many (arXiv 2512.10159). That is exactly the skill Chapter 1 teaches, so check the signs in every AI answer.
• The quiz at the next session 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.