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Current Electricity · Tier 3 · Topic 11 of 12

V–I Characteristics & Limitations of Ohm's Law

Ohm's law is not a law of nature. It is a description that fits many materials over a limited range — and the devices that break it are the ones modern electronics is built from.

NCERT §3.6 · Points to Ponder 2 · fully in syllabus · graph identification

Part 1 · The idea, told simply

Everyone learns V = IR and assumes it is Ohm's law. It is not. Getting this distinction right is worth a mark on its own, because NCERT puts it in Points to Ponder and NEET asks it.

V = IR is a definition. Ohm's law is a claim.

V = IR simply defines resistance as the ratio of voltage to current. You can apply it to any conducting device whatsoever — a diode, a bulb filament, a lump of GaAs. Measure V, measure I, divide, and you have a number called R at that operating point.

Ohm's law is the extra, much stronger claim that this R comes out to the same number every time — that R does not depend on V. Equivalently, that the plot of I against V is a straight line.

NCERT states it exactly: "The assertion that V = IR is a statement of Ohm's law is not true. This equation defines resistance and it may be applied to all conducting devices whether they obey Ohm's law or not. The Ohm's law asserts that the plot of I versus V is linear i.e., R is independent of V."

Story track · what a straight line is promising you

Think of a shop that charges by weight. If a kilo of rice costs ₹50, then two kilos cost ₹100 and three cost ₹150. Plot cost against weight and you get a perfect straight line through the origin. The rate — ₹50 per kilo — never changes.

An ohmic resistor behaves like that shop. Double the voltage, double the current. The "rate", R, is fixed.

Now imagine a shop with bulk discounts, a minimum charge, and different prices for buying versus returning. Cost against weight is no longer a straight line at all. You can still work out a price-per-kilo at any particular purchase — but it is a different number each time. That is a non-ohmic device.

Animation 1 · Ohmic and non-ohmic, side by side

Move the operating point. Watch R = V/I stay fixed on one curve and wander on the other.

Part 2 · The three ways Ohm's law fails

NCERT §3.6 lists exactly three types of deviation. Learn them as a numbered set, because questions ask "which type does this device show".

TypeWhat goes wrongNCERT figureExample
(a)V ceases to be proportional to I — the graph bendsFig. 3.5a good conductor at high current; ρ rising with I
(b)The relation depends on the SIGN of V — reversing V does not give the same magnitude of currentFig. 3.6a diode
(c)The relation is not UNIQUE — more than one value of V gives the same IFig. 3.7GaAs

NCERT adds two useful notes: a rectifier combines features (a) and (b), and an example of (a) is when ρ increases with I even if the temperature is kept fixed — so it is not merely a heating effect.

Animation 2 · The three failure modes

Step through each one and see precisely what breaks.

Type (b) in detail: the diode

Story track

A diode is a one-way valve for current. Push it forwards and current flows easily. Push it backwards with the same voltage and almost nothing gets through.

NCERT's Fig. 3.6 makes a point that is easy to miss and is directly examinable: the scales for the negative and positive values of voltage and current are different. The forward axis runs in milliamperes and tenths of a volt; the reverse axis runs in microamperes and whole volts. If both halves were drawn on the same scale, the reverse branch would look like a flat line along the axis.

Forward: about 0.2 V gives about 1.5 mA → R ≈ 133 Ω Reverse: about 2 V gives a few μA → R ≈ 10⁵ Ω or more The SAME device, with resistances differing by a factor of thousands

Animation 3 · The diode, and the scale trick

Toggle between the textbook's split scales and a single honest scale. The shape changes completely.

Type (c) in detail: GaAs and non-uniqueness

This is the strangest of the three. In gallium arsenide, the current rises with voltage, then falls as the voltage keeps rising, then rises again. The falling stretch is called a negative resistance region, and because of it a single value of current can correspond to several different voltages.

Animation 4 · One current, three voltages

Slide the horizontal line. Where it cuts the curve more than once, the relation is not unique.

Part 3 · Reading slopes without getting caught

Check the axes before you quote a slope
V on the vertical axis, I on the horizontal → slope = ΔV/ΔI = R I on the vertical axis, V on the horizontal → slope = ΔI/ΔV = 1/R

So on a V–I plot a steeper line means a larger resistance, but on an I–V plot a steeper line means a smaller one. Examiners draw both and rely on the confusion. Read the axis labels first, every time.

Animation 5 · The same two resistors, two sets of axes

Swap the axes and watch which line looks "steeper" change places.

Maths track · the local statement of Ohm's law

NCERT Points to Ponder 2 gives a second, deeper way to say the same thing. From E = ρj,

a conducting material obeys Ohm's law when its resistivity does NOT depend on the magnitude and direction of the applied electric field

This is more demanding than "V is proportional to I", and it explains all three failure modes at once. If ρ grows with the field strength, you get type (a). If ρ differs for the two field directions, you get type (b). If ρ behaves so oddly that several fields give the same j, you get type (c).

It also connects back to the drift derivation of Topic 3, which assumed τ and n were constants independent of E. Ohm's law holds exactly as long as that assumption holds — and NCERT notes that if the field becomes too strong, there are departures from Ohm's law in all cases.

Non-ohmic does not mean useless

Quite the reverse. NCERT is explicit: materials and devices not obeying Ohm's law are actually widely used in electronic circuits. A resistor that faithfully obeys Ohm's law can only ever scale a signal. A diode, which breaks it, can rectify; a device with a negative resistance region can oscillate. The failures are the useful part.

Trap · the six that cost marks
  1. Calling V = IR "Ohm's law". It is the definition of resistance and applies to every device.
  2. Saying a diode has no resistance. It has a resistance at every point — it just is not constant.
  3. Quoting a slope without checking the axes. V–I gives R; I–V gives 1/R.
  4. Assuming type (a) is always a heating effect. NCERT's example holds at fixed temperature.
  5. Thinking non-ohmic devices are defective or rare. They are the basis of all electronics.
  6. Forgetting that the two halves of a diode graph use different scales.

Part 4 · Formula sheet

The distinction that gets examined

V = IR DEFINES resistance · valid for ALL conducting devices Ohm's law ASSERTS that R is independent of V ⇔ the I–V plot is a straight line through the origin A device obeying it is OHMIC; one that does not is NON-OHMIC

The three deviations (NCERT §3.6)

(a) V ceases to be proportional to I → curve bends (Fig. 3.5) (b) the relation depends on the SIGN of V → diode (Fig. 3.6) (c) the relation is NOT UNIQUE, several V for one I → GaAs (Fig. 3.7) A rectifier combines (a) and (b) Example of (a): ρ rises with I even at FIXED temperature

Reading graphs

V–I plot (V vertical): slope = R steeper ⇒ LARGER R I–V plot (I vertical): slope = 1/R steeper ⇒ SMALLER R Ohmic device: straight line through the origin Non-ohmic device: any curve, kink, or asymmetry R at any point = V/I at that point (the chord, not the tangent)

The diode

Forward bias: small V, large I → low resistance (≈ 10² Ω) Reverse bias: large V, tiny I → high resistance (≈ 10⁵ Ω or more) NCERT Fig. 3.6 uses DIFFERENT SCALES for the two halves forward: milliamperes and tenths of a volt reverse: microamperes and whole volts

The local statement

E = ρ j A material obeys Ohm's law when ρ does not depend on the MAGNITUDE or the DIRECTION of the applied electric field Homogeneous conductors obey it within some range of field values If the field becomes too strong, all materials depart from it

Sanity checks

Ohm's law is not a fundamental law of nature Any curve through the origin that is not straight ⇒ non-ohmic Asymmetry about the origin ⇒ non-ohmic, type (b) Non-ohmic devices are widely used, not defective Always read the axis labels before quoting a slope

Part 5 · 50 NEET-pattern questions with full solutions

Graph-heavy by nature — this topic is mostly curve identification. Includes 6 graph-based questions, 3 assertion–reason questions, and 9 tagged Failure mode on the three deviations. Year labels are not attached: the patterns are authentic, the wording is mine.