Systematic Reduction of Resistor Circuits
Ideal wires have zero voltage drop. Elements are parallel only if both endpoints match, and series only if their shared node has no other branch; after reduction, Ohm law recovers local quantities.
Why this shows up in the exam
Figure-based equivalent resistance · Finding one branch current · Short-circuit and open-circuit simplification
Learn the idea
Redraw by nodes, reduce what is truly series or parallel, then recover requested currents and voltages. Complicated drawings often hide simple electrical connections. Wires make every point on a node equipotential, so topology matters more than the page shape.
🧠 Memory hook: Trace nodes, not shapes.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- V = I R — element relation for an ideal resistor
- R_eq by valid series/parallel steps — equivalent seen at the chosen terminals
- I_branch = Delta V_branch/R_branch — branch current after node voltages are known
How to approach it
- 1Label equipotential nodes
- 2Reduce only verified series or parallel groups
- 3Back-substitute for the requested branch
Common slip-ups that cost marks
- •Calling crossing lines connected without a junction
- •Combining elements that share only one node in parallel
- •Stopping at R_eq when a branch quantity is asked
🌟 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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