Resistance from Resistivity and Geometry
For a homogeneous uniform conductor with constant cross-section and resistivity, resistance is rho L/A. Nonuniform conductors require summing differential elements dR = rho dl/A(l).
Why this shows up in the exam
Designing wires and cables · Hollow or tapered conductors · Concentric-shell radial resistance
Learn the idea
A uniform conductor resists more when it is longer, less when it is thicker, and according to its material resistivity. Charge must travel farther through a long wire and has more parallel microscopic paths in a thick wire. Resistivity captures material and temperature; L/A captures geometry.
🧠 Memory hook: Material rho times path length, divided by conducting area.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- R = rho L/A — uniform conductor at a specified temperature
- dR = rho dl/A(l) — series differential element for varying area
- R = integral rho dl/A(l) — nonuniform path with known geometry
How to approach it
- 1Draw the current path
- 2Identify the area normal to current
- 3Integrate if area varies along the path
Common slip-ups that cost marks
- •Using total surface area instead of cross-section
- •Applying rho L/A directly to radial flow
- •Changing rho when only shape changes
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
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