Question
A student performs an experiment to verify Ohm’s Law. She measures voltage V (in volts) across a resistor and current I (in amperes) through it, recording the following:
| V (V) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| I (A) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 |
(a) Plot the V–I graph. What does its shape tell us? (b) Calculate the resistance R from the graph. (c) Give one example of a non-ohmic conductor.
Solution — Step by Step
Take V on the x-axis and I on the y-axis (this is the NCERT convention — many students accidentally swap them). Plot the five points: (1, 0.1), (2, 0.2), (3, 0.3), (4, 0.4), (5, 0.5). Join them — they fall perfectly on a straight line passing through the origin.
A straight line through the origin means V and I are directly proportional — double the voltage, double the current. This is exactly what Ohm’s Law states: the ratio V/I stays constant for a given conductor at constant temperature. That constant ratio is the resistance R.
The slope of the V–I graph gives us R. Pick any two points on the line, say (2, 0.2) and (4, 0.4):
Or just use any single data point: . Either way, R = 10 Ω.
A diode (p-n junction) is the classic non-ohmic example. Its V–I graph is a curve, not a straight line — the resistance changes depending on how much voltage you apply. Another NCERT-accepted answer: a filament bulb (tungsten filament heats up, so R changes with temperature).
Why This Works
Ohm’s Law says that for a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it. Write it as , where R is a constant. The “constant temperature” condition is key — resistance changes when temperature changes.
The V–I graph being a straight line through the origin is a visual proof of this proportionality. The steeper the line, the higher the resistance (more voltage needed per unit current). A horizontal line would mean zero resistance; a vertical line would mean infinite resistance.
Non-ohmic conductors don’t follow this neat relationship. In a diode, the current shoots up exponentially once voltage crosses a threshold — the graph curves sharply. In a tungsten bulb, the filament heats to ~2500°C, massively increasing its resistance, so the graph curves downward.
Alternative Method
Instead of plotting V on x-axis and I on y-axis, some textbooks plot I on x-axis and V on y-axis. In that case:
The slope still gives R. Do not confuse this with the I–V graph, where slope = 1/R (conductance). NCERT Class 10 uses the V–I convention; Class 12 problems sometimes use I–V. Always check which axis is which before calculating.
Quick check: if V is on the x-axis and the line slopes gently (small angle), R is small. If the line is steep, R is large. Visualising this saves time in MCQs.
Common Mistake
The most common error: students write “slope of V–I graph = 1/R” instead of R. This happens when they confuse the V–I graph (slope = R) with the I–V graph (slope = 1/R). In CBSE boards and NCERT practicals, the standard graph has V on x-axis and I on y-axis, so slope = ΔI/ΔV = 1/R. But NCERT Class 10 Chapter 12 explicitly says “V–I graph is a straight line” and asks you to find R as the ratio V/I, not the slope of that specific orientation. Read the question carefully — if V is on x-axis, slope = ΔI/ΔV = 1/R; if V is on y-axis, slope = ΔV/ΔI = R. Getting this backwards costs full marks on a 3-mark question.
- V in volts (V), I in amperes (A), R in ohms (Ω)
- Slope of V–I graph (V on y-axis)
- Slope of I–V graph (I on y-axis) (conductance)
- Ohmic: straight line through origin
- Non-ohmic: curve (diode, filament bulb, LED)