--- title: "Current from source in ladder circuit" subject: "Basic Electrical Engineering" chapter: 2 key: "semester_1/basic_electrical_engineering:source-current-3v-2ohm-ladder" source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/source-current-3v-2ohm-ladder site: BCT Engineering --- # Current from source in ladder circuit Basic Electrical Engineering · Chapter 2: DC circuits - Asked in: 2073 Shrawan, 6 marks - Video: [Equivalent Resistance of a Ladder Network](https://www.youtube.com/watch?v=dUwO96_p62w) — Electric Circuits - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/source-current-3v-2ohm-ladder - Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-2 ## Question Find current from the source in the following circuit diagram. [Figure: 3 V source with 1 Ω in parallel; three 2 Ω series resistors along the top; a 1 Ω resistor and a 5 Ω resistor in the shunt branches.] ## Short answer A short circuit across the 1 Ω resistor bypasses it and the last branch. The circuit simplifies to 2 Ω in series with the parallel combination of 2 Ω and 2 Ω (effective 1 Ω). Total resistance is 3 Ω, so source current I = 3 V / 3 Ω = 1 A. ## Answer #### Reading the figure A 3 V source feeds a ladder: series 2 Ω, then node N₁ with a 2 Ω shunt, series 2 Ω to node N₂, then series 2 Ω and 5 Ω. The 1 Ω shunt at N₂ has a wire connected across it (from its top to the bottom rail), so N₂ is shorted to the bottom rail. The 1 Ω carries no current, and the last 2 Ω + 5 Ω branch is also at zero potential difference. #### Reduction - From N₁ to the bottom rail: the 2 Ω shunt in parallel with the 2 Ω series leg leading to the short at N₂. 2 ∥ 2 = 1 Ω - Total resistance seen by the source = 2 Ω (first series) + 1 Ω = 3 Ω #### Source current I = 3/3 = 1 A **Answer: Source current = 1 A** Assumption: the loop of wire drawn round the 1 Ω is a short circuit. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the wire drawn across the 1 Ω shunt at N2 do? A. Doubles the current in the 1 Ω B. Opens the circuit at N2 C. Shorts N2 to the bottom rail so the 1 Ω carries no current D. Adds 1 Ω in series with the ladder Answer: C. A short circuit bypasses the 1 Ω; N2 is at the same potential as the bottom rail. (Key point: Effect of the wire) 2. Why does the last 2 Ω + 5 Ω branch carry no current? A. 5 Ω is too large B. Both its ends are at the same potential (rail) C. It is in series with the source D. It has a capacitor Answer: B. With N2 shorted to the rail, there is zero potential difference across that branch. (Key point: Last branch) 3. From N1 to the bottom rail the resistance is A. 2 Ω shunt in parallel with 2 Ω series leg = 1 Ω B. 2 + 2 = 4 Ω C. 2 + 5 = 7 Ω D. 0.5 Ω Answer: A. The series 2 Ω leads to the short, so it is in parallel with the shunt 2 Ω: 2 || 2 = 1 Ω. (Key point: Resistance from N1) 4. Total resistance is 2 + 1 = 3 Ω. The source current is A. 1.5 A B. 3 A C. 9 A D. 1 A Answer: D. I = V/R = 3 V / 3 Ω = 1 A. 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