Current Electricity Ā· Question-type card
Eight archetypes that recur in this sub-topic, ranked by how often they actually appear. Three of them ā wire stretching, the temperature behaviour of Ļ, and VāI slopes ā cover most of what NEET realistically asks from this card.
The one that appears almost every year
Volume stays constant, so stretching to n times the length thins the wire at the same time. Resistance rises on both counts ā and the combined effect is far steeper than students expect.
Stretching to twice the length quadruples the resistance: R ā nĀ². The area halves and the radius drops to 1/ā2 of its original value ā but resistivity never changes, because the material is the same.
For a fixed amount of material, volume is constant, so length and area move together. Every stretching and cutting problem is a special case of the chain below ā and Ļ, the material property, sits it all out.
Three archetypes cover most of what is realistically asked from this exact card. Secure these before touching the rest.
R \u221d \u2113\u00b2 \u221d 1/r\u2074 for stretching; R/n\u00b2 for n parts rejoined in parallel.\u03c4 falls, so \u03c1 rises. Semiconductors: n rises faster, so \u03c1 falls. The favourite assertion\u2013reason contrast.V/I from dynamic dV/dI, and ohmic from non-ohmic.