Classification of Elements: Unilateral and bilateral elements

Classification of Elements: Unilateral and bilateral elements

1. What Bilateral vs Unilateral Means (based on V-I relation symmetry)

• Bilateral element: V-I characteristic is same for both directions of current; property does not change when terminals are interchanged or current reversed. Symmetric $V-I$ through origin.
  • Examples: Resistor, inductor, capacitor (linear $R,L,C$), uniform wire.
  • Test: if you reverse $I$ to $-I$, you get $V$ to $-V$ (odd symmetry for $R$: $V=IR ⇒ -V$). Linear bilateral holds $V/I$ = constant both ways.
• Unilateral element: V-I depends on direction; asymmetric. Interchanging terminals or reversing current changes characteristic.
  • Examples: Diode (p-n), transistor, ideal voltage source with diode, Gunn diode — conducts one way, blocks other.
  • Test: diode $I=0$ for $V<0$ (reverse), $I=I_0(e^{V/V_T}-1)$ for $V>0$ ⇒ not symmetric.

2. Why Classification Matters

Determines if superposition/reciprocity techniques apply (bilateral needed for some theorems). Bilateral + linear ⇒ superposition holds; unilateral ⇒ not.

3. Worked Checks

(a) Resistor 10Ω: V=10V→I=1A; V=-10V→I=-1A ⇒ bilateral ✓

(b) Diode: V=0.7V→I~1mA; V=-0.7V→I≈-1nA (reverse leakage) ⇒ unilateral ✓

(c) Battery ideal voltage source 5V: V=5V independent of I direction? Actually unilateral? Ideal source not bilateral because V fixed not proportional to I, but classification as active bilateral? Usually source considered active, not classified as bilateral/unilateral but unilateral in sense? Exam expects diode as unilateral example, R as bilateral.

4. Exam Points

• Define bilateral (same both directions) vs unilateral (direction-dependent) with $V-I$ sketch — 5 marks, very frequent (almost certain to ask with diode vs resistor example).
• Give 2 examples each — 3-5 marks, frequent.
• Mention that $R,L,C$ are bilateral (if linear) — 3 marks.