Chapter 2

Fundamental Laws

Chapter 1 gave you current, voltage and power. None of that solves a circuit. This chapter adds the three laws that do — Ohm's law for one device, KCL for a node, KVL for a loop — and the recognition skills that keep the algebra small: which drawn points are really one node, which resistors are really in parallel, and which port a resistance actually belongs to. Nine exercises below.

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What you need before you start

Ohm's law is a device law: across an ideal resistor the voltage drop is proportional to the current, and the constant is the resistance.

v(t) = i(t) R Ω = V/A

The fine print — this is true only in the passive sign convention: i has to enter the resistor at its + terminal. Draw the arrow the other way and the law needs a minus sign.

Both limits are real components. R → ∞ passes no current (i = 0) — that is an open. R = 0 develops no voltage (v = 0) — that is a short. Conductance G = 1/R S swaps the two: G = 0 is the open.

KCL is charge conservation at a junction. The book picks one of the three equivalent phrasings and never switches — do the same.

Σ i_n(t) = 0 A

“The sum of all currents leaving a node is equal to zero.” A current leaving is positive, a current entering is negative. Some of them come out negative; that is the point.

KVL is energy conservation around a walk.

Σ v_n(t) = 0 V

“The sum of all voltages around a closed path is zero.” A closed path only has to start and end at the same point — wires optional, so a loop may close straight across a pair of open terminals. Signs, three rules: start at the loop's lowest-left corner, go clockwise, take the first voltage sign you meet on each element.

Lowercase means time. v and i are quantities that may vary with time; V and I are reserved for the constant DC case. The three laws above are written in lowercase because they hold at every instant, not only in steady state — every circuit in this chapter happens to be DC, so you will see both spellings.

voltage current power

“Remember that a bad solution plan is better than no plan at all.”

§2.9. From here on there is more than one legal way to start, and the cheap one is usually the loop with a single unknown in it. Several exercises below grade the plan — which loop, which pair, which port — before they grade the arithmetic.

Exercises

Each one names where it comes from in the book. § is the section sign, so “§2.6” means section 2.6; “Ex. 2.6.1” is a worked example inside that section, and “Fig.” a figure.