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Length and Area
Resistance of a uniform wire depends on length and cross-sectional area through R = ρL/A.
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Length and Area
A long thin wire resists current more.
A short thick wire resists current less.
Recommended for Class 10
Length and Area
The resistance of a uniform wire depends on its dimensions.
For a wire:
**R = ρL/A**
where:
0 = resistance;
0 = resistivity of the material;
0 = length;
0 = cross-sectional area.
Effect of Length
R ∝ L
A longer wire has greater resistance because charge carriers experience more interactions while moving through the longer path.
If length doubles:
R doubles, provided other factors stay constant.
Effect of Area
**R ∝ 1A**
A thicker wire has lower resistance because it provides more conducting cross-sectional area.
If area doubles:
R halves, for the same material and length.
Length and Area — Advanced
The geometrical dependence of resistance follows from resistivity. For a homogeneous conductor, resistance scales linearly with path length and inversely with available cross-sectional area.
Common Mistakes
Common Mistakes
- Mistake
Thickness means cross-sectional area, not merely visual width.
- Mistake
Longer wire → higher R.
- Mistake
Thicker wire → lower R.
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Practice
PQ
Q1. State resistance equation.
PQ
Q2. Effect of doubling length.
PQ
Q3. Effect of doubling area.
PQ
Q4. Why thick wires have less resistance.
PQ
Q5. Compare two identical-material wires of different length.
Exam Practice
EQ
Q1. Explain effect of length.
EQ
Q2. Explain effect of area.
EQ
Q3. State `R=ρL/A`.
EQ
Q4. Define resistivity symbolically.
EQ
Q5. Calculate ratio when length doubles and area halves.
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.