AoNArt of Nanoelectronics
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01 · Introductory

Reference directions for voltage and current

An arrow defines the positive direction of a variable; it does not predict the answer.

70-95 minIntroductory
In this lesson
  • Define a voltage reference with an arrow from negative to positive.
  • Define a current reference direction.
  • Interpret a negative result without changing the model.
  • Relate VAB to node potentials.
Starting question

If you draw a current arrow to the right and later obtain I=−2 mA, should you erase the arrow and redraw it?

No. A reference arrow is like the positive direction of a coordinate axis: it defines how a signed number will be interpreted before the physical answer is known.

01.1Physics first, sign second

A branch can carry a physical current and two nodes can possess a physical potential difference before we decide how to name those quantities. The reference choice turns that physical state into a signed variable.

This distinction is important: the arrow does not force nature to follow it. It only tells us what a positive numerical answer would mean.

01.2Voltage reference: tail is negative, head is positive in AoN

Figure 1.1 — Voltage and current referencesThe voltage arrow B→A defines VAB = VA − VB. The current arrow simply defines the positive direction of I.
BAVAB−+I

AoN defines the voltage arrow from the negative reference toward the positive reference. B→A therefore means

VAB = VA − VB

If VAB=−3 V, then B is 3 V above A. The arrow remains exactly where it was; the negative sign carries the information.

01.3Current reference: one arrow, one positive direction

The current arrow gives the positive reference direction. A result I=+4 mA means the conventional current follows the arrow. A result I=−4 mA means the same magnitude flows opposite to it.

I = −4 mA   ⇒   |I|=4 mA opposite to the reference arrow

01.4Two engineers can choose opposite references and still agree

Suppose engineer 1 defines current left→right as I1, while engineer 2 defines right→left as I2. For the same physical branch flow,

I2 = −I1

Likewise, VBA=−VAB. The signed variables differ, but the physical state does not.

This is why circuit equations are reliable only when the reference definitions are carried with the symbols.

01.5Reference choices are bookkeeping freedoms, not arbitrary physics

You are usually free to choose a convenient direction for an unknown current or voltage. What is not free is changing that choice halfway through a derivation without changing the variable definition.

A good schematic therefore shows the reference before the equation. A good solution keeps it fixed until the final interpretation.

VAB=−7 V. What is VBA?
+7 V, because reversing the voltage reference reverses the sign.

01.6Practice for mastery

  1. An arrow defines current A→B and the meter result is −12 mA. State the physical current in words.
  2. VA=1.5 V and VB=4.0 V. Find VAB and VBA.
  3. Two students choose opposite current arrows. One obtains +6 mA. What should the other obtain if both are correct?
  4. Explain why a negative value is often evidence of a good reference convention rather than a mistake.
Solutions

1. 12 mA flows B→A.

2. VAB=−2.5 V and VBA=+2.5 V.

3. −6 mA.

4. Because the reference was chosen before the unknown physical direction was known; the sign tells which direction nature actually selected.

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