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Find R when branch DA current is zero

Short answer

Bridge balance with zero current in DA requires R = 2 Ω. Total resistance is 4 Ω, source current 5 A, voltage across bridge 10 V, so current through R = 10/(2+2) = 2.5 A.

In the network shown below, find the value of resistance R and the current through it when the current through branch DA is zero. [Figure: triangle ABC with centre node D; 2 Ω in AB, 2 Ω in AC, resistance in DA; 2 Ω in DB, R in DC; 20 V source and 2 Ω in BC.]

Reading the figure

Triangle ABC with centre D. Branches: A–B = 2 Ω, A–C = 2 Ω, D–B = 2 Ω, D–C = R (unknown), D–A (some resistance, its value is not needed). Between B and C: a 20 V battery in series with 2 Ω.

This is a Wheatstone bridge with the supply across B and C. The branch DA is the detector. No current in DA means V_D = V_A.

Balance condition

R_BA/R_AC = R_BD/R_DC

2/2 = 2/R

R = 2 Ω

Current in R

Two parallel paths from B to C:

  • B–A–C: 2 + 2 = 4 Ω
  • B–D–C: 2 + 2 = 4 Ω

Bridge resistance = 4 ∥ 4 = 2 Ω

Total resistance = 2 (bridge) + 2 (series resistor) = 4 Ω

Source current = 20/4 = 5 A

Voltage across the bridge = 5 × 2 = 10 V

Current through R = 10/(2 + 2) = 2.5 A

Answer: R = 2 Ω; current through R = 2.5 A

✓ Answer checked by Claude Opus 5.5 (high effort)

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