Uniform Wire Loops, Arcs, and Polygons
For a uniform wire of total resistance R, an arc occupying fraction f has resistance fR. Two complementary arcs between taps are parallel; polygon sides are handled by their two path lengths when symmetry permits.
Why this shows up in the exam
Bent circular wires · Polygonal wire loops · Tapped uniform resistance wire
Learn the idea
A uniform loop between two taps becomes two arc resistances in parallel. Current injected at one point of a loop can reach the exit along either arc. Arc resistance follows arc length, and the two routes share the endpoint voltage.
🧠 Memory hook: Split the loop into two length-proportional paths, then parallel them.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- R_arc = R(theta/2pi) — uniform circular wire arc subtending theta
- R_eq = R₁ R₂/(R₁+R₂) — two complementary arcs in parallel
- R_adjacent = R(n-1)/n² — adjacent vertices of a uniform n-sided loop with total resistance R
How to approach it
- 1Compute total post-reshaping resistance
- 2Split by length or angle
- 3Combine the two endpoint paths in parallel
Common slip-ups that cost marks
- •Treating arcs as series
- •Using angle in degrees without a consistent fraction
- •Forgetting resistance changed when the wire was stretched first
🌟 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.
More from Current Electricity
Resistivity, Conductivity, and Material Properties
Learn how resistivity and conductivity depend on material, length, area, and how resistance changes with dimensions and temperature.
Series and Parallel Combinations of Resistors
Master the calculation of equivalent resistance, voltage division, and current distribution in series and parallel resistor networks.
Electrical Energy, Power, and Heating Effect
Calculate electrical energy, power dissipation, and understand the heating effect of current in various circuit configurations.
EMF, Internal Resistance, and Terminal Voltage
Understand the concepts of EMF, internal resistance of cells, and how terminal voltage is affected in real circuits.
Drift Velocity and Microscopic View of Current
Explore the microscopic origin of current, including drift velocity, relaxation time, current density, and the effect of electric field in conductors.
Kirchhoff's Laws and Circuit Analysis
Apply Kirchhoff's current and voltage laws to analyze complex circuits and solve for unknowns.