Which one of the following graphs correctly represents the current (I) – voltage (V) variation for a rectangular piece of a semiconductor wafer ?

Q: What is the answer to NDA (II) 2023 GAT Q59?

A. Correct — A, the straight line through the origin. The item describes a **rectangular piece of a semiconductor wafer** — a plain slab of material with two contacts, not a device with a junction in it. Over the ordinary range of voltages such a slab behaves as a simple resistor: doubling the voltage doubles the current, so I is proportional to V and the graph is a straight line passing through the origin. The word 'semiconductor' is the trap. What makes a semiconductor device non-ohmic is the **p–n junction**, not the material. A diode conducts freely one way and blocks the other, which is why its characteristic is the steeply sweeping curve of option (c). A uniform wafer has no junction and therefore no such asymmetry. So the printed answer is the ordinary ohmic straight line.

(a)A straight line through the origin, I rising in proportion to V
(b)A straight line of negative slope, I falling as V rises
(c)A curve that stays near zero and then sweeps steeply upward
(d)A curve that starts high and decays towards zero as V rises

Answer

Why

Correct — A, the straight line through the origin. The item describes a rectangular piece of a semiconductor wafer — a plain slab of material with two contacts, not a device with a junction in it. Over the ordinary range of voltages such a slab behaves as a simple resistor: doubling the voltage doubles the current, so I is proportional to V and the graph is a straight line passing through the origin.

The word 'semiconductor' is the trap. What makes a semiconductor device non-ohmic is the p–n junction, not the material. A diode conducts freely one way and blocks the other, which is why its characteristic is the steeply sweeping curve of option (c). A uniform wafer has no junction and therefore no such asymmetry.

So the printed answer is the ordinary ohmic straight line.

Why the others are wrong

(b)
A straight line of negative slope, I falling as V rises — A negative slope would mean current flowing backwards as the applied voltage increases. No passive resistive element behaves this way; resistance is a positive quantity.
(c)
A curve that stays near zero and then sweeps steeply upward — This is the forward characteristic of a p–n junction DIODE, which passes almost nothing until the threshold and then conducts sharply. A plain rectangular wafer has no junction, so it shows no threshold.
(d)
A curve that starts high and decays towards zero as V rises — This has the current falling away as voltage increases, which no simple resistive sample does. It does not correspond to any standard characteristic of a uniform semiconductor slab.

Concept

An element is ohmic when V = IR holds with R constant, giving a straight I–V line through the origin. A uniform piece of conductor or semiconductor is ohmic within normal limits. Non-ohmic behaviour comes from structure rather than substance — a p–n junction, a gas discharge, or a filament whose resistance changes as it heats.

The question separates candidates who read 'semiconductor' and reach straight for the diode curve from those who notice the words 'rectangular piece' and 'wafer'. A slab of silicon with a contact at each end is just a resistor made of silicon. It becomes a device only when a junction is formed inside it. Ask what structure is present, not what the material is called.

Key facts

Ohmic: V = IR with R constant, giving a straight line through the origin.
A uniform semiconductor slab is ohmic over ordinary voltages.
Non-ohmic behaviour comes from a junction, not from the material.
A p-n junction diode gives the sharply rising threshold curve.
Semiconductor resistance falls as temperature rises, unlike a metal's.

Slab versus junction

Rectangular semiconductor wafer→No junction — behaves as a resistor, straight I–V through the origin

p–n junction diode→Conducts one way past a threshold — sharply curved I–V

Metal wire→Also ohmic, straight I–V line

It is the junction, not the word 'semiconductor', that bends the graph — option (a).

Study next

Ohmic and non-ohmic conductorsI–V characteristics of a p–n junction diodeIntrinsic and extrinsic semiconductorsWhy a semiconductor's resistance falls with rising temperature

Common traps

Assuming anything labelled 'semiconductor' must give a diode curve.
Overlooking 'rectangular piece', which signals a plain slab with no junction.
Confusing the material with the device built from it.

NDA prints four I–V shapes and names a component — decide first whether the component contains a junction; without one, the answer is the straight ohmic line.

Related PYQs

NDA_GAT_2018_I_Q602018Open & attempt →

Which one of the following devices is non-ohmic ?

(a) Conducting copper coil
(b) Electric heating coil
(c) Semi conductor diode
(d) Rheostat

Answer(c) Semi conductor diode

The exact companion: it asks which device is NON-ohmic, and the official answer is the semiconductor diode. That is the junction device whose curve is option (c) here — while the plain wafer in this item stays ohmic.

Practice

practice — not a real PYQ
The I–V characteristic of a p–n junction diode in forward bias is
- (a)a straight line through the origin
- (b)a straight line with negative slope
- (c)a curve rising sharply after a threshold voltage
- (d)a horizontal line
Answer(c) a curve rising sharply after a threshold voltage — the junction blocks conduction until the barrier is overcome.
practice — not a real PYQ
Which one of the following is an ohmic conductor?
- (a)A p–n junction diode
- (b)A copper wire at constant temperature
- (c)A gas discharge tube
- (d)A transistor
Answer(b) A copper wire at constant temperature — its resistance stays constant, giving a straight I–V line.