Ohm's Law and Resistivity
Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant. Resistivity is the material property that measures how strongly a substance opposes current flow.
In one line: Resistance belongs to a piece of wire; resistivity belongs to the material.
Concept Practice Coming SoonUnderstand it
- For an ohmic conductor at constant temperature, V/I remains constant and is called resistance R.
- Resistance depends on dimensions, while resistivity depends on the material and temperature.
- In the microscopic model of a metal, resistivity is related to electron mass, number density, charge, and relaxation time by ρ = m/(ne2τ).
- For metals, resistivity generally increases with temperature because collisions become more frequent and relaxation time decreases.
Example
Formula and rule
Ohm's law: V = IR, where V is potential difference in volt, I is current in ampere, and R is resistance in ohm.
Resistivity relation: R = ρL/A, where ρ is resistivity in ohm metre, L is length in metre, and A is area in m2.
Microscopic form for metals: ρ = m/(ne2τ).
Use Ohm's law only when temperature, strain, and other physical conditions are constant.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
A wire of length 2.0 m and area 0.50 × 10−6 m2 has resistivity 1.7 × 10−8 ohm m.
- 1Its resistance is R = ρL/A = (1.7 × 10−8 × 2.0)/(0.50 × 10−6) ohm = 0.068 ohm.
- 2If 0.34 V is applied, current I = V/R = 0.34/0.068 = 5.0 A.
Method you can reuse
- 1Check whether the conductor is ohmic and temperature is constant.
- 2Choose V = IR for circuit values or R = ρL/A for material and dimension values.
- 3Convert area to m2.
- 4Substitute values with units.
- 5Interpret whether larger length increases resistance and larger area decreases it.
Sketch it in your answer
Draw a V-I graph with V on the vertical axis and I on the horizontal axis. For an ohmic conductor, show a straight line through the origin. Label slope as R. For non-ohmic behaviour, the graph is curved and V/I is not constant.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
What does the slope of a V-I graph represent for an ohmic conductor?
Think first, then show answerHide answer
Common wrong answer
Using ρ = RA/L with area in mm2 without converting to m2 gives an answer off by a large factor.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant. Resistivity is the material property that measures how strongly a substance opposes current flow.
- 2
Add for 2 marks
Example: A nichrome wire shows higher resistance than a copper wire of the same length and area because nichrome has greater resistivity. This is why nichrome is used in heating elements.
- 3
Add for 3 marks
For an ohmic conductor at constant temperature, V/I remains constant and is called resistance R.
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