Bridge and Delta-Star Network Reduction
A delta-star transformation preserves resistance seen between all three external terminals. Each star arm equals the product of the two adjacent delta arms divided by the sum of all delta arms.
Why this shows up in the exam
Triangular-pyramid networks · Bridged resistor webs · Networks with a current-independent branch
Learn the idea
Non-series-parallel networks require balance conditions, node equations, or delta-star conversion. Some resistor webs cannot be peeled into obvious series and parallel pieces. A balanced link may carry no current; otherwise a three-terminal delta can be replaced by an equivalent star.
🧠 Memory hook: If series-parallel stalls, look for balance, symmetry, or delta-star.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- R_A = R_AB R_CA/(R_AB+R_BC+R_CA) — delta-to-star arm connected to node A
- P/Q = R/S — balanced bridge condition for a zero-current detector branch
How to approach it
- 1Redraw and label nodes
- 2Test balance or symmetry
- 3Transform one three-terminal section and re-reduce
Common slip-ups that cost marks
- •Forcing crossed branches into series
- •Applying bridge balance to the wrong four arms
- •Using delta-star without preserving the three terminals
🌟 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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