Parallel Resistors and Current Division
For ideal resistors connected between the same two nodes, conductances add. In two branches, current through one branch is inversely related to its own resistance.
Why this shows up in the exam
Shunts · Household parallel loads · Parallel wire bundles
Learn the idea
Parallel branches share voltage and split current according to conductance. Each parallel path begins and ends at the same two nodes, so each sees the same voltage. Lower resistance draws more current.
🧠 Memory hook: Same voltage in parallel; current prefers lower resistance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- 1/R_eq = sum(1/R_i) — parallel equivalent resistance
- I_i = V/R_i — branch current under common parallel voltage
- I₁/I₂ = R₂/R₁ — two-branch current division
How to approach it
- 1Label the two end nodes
- 2Combine conductances
- 3Use common voltage to recover branch currents
Common slip-ups that cost marks
- •Adding resistances directly in parallel
- •Assuming current divides equally for unequal branches
- •Calling elements parallel without checking both nodes
🌟 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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