Skip to main content

Unknown R when branch OC current zero

Short answer

The bridge balances when current in OC is zero: 1/1.5 = 4/R, giving R = 6 Ω. Total circuit resistance is 4 Ω, source current 2.5 A, so the current through the 4 Ω–6 Ω path (and hence R) is 0.5 A.

Calculate the value of unknown resistance R in the circuit shown below and the current flowing through it when the current in the branch OC is zero. [Figure: triangle ABC with centre O; 4 Ω in arm CO... branch C to A has 1 Ω, branch C to B 1.5 Ω, 4 Ω in branch CO, R in branch OB, 4 Ω in branch OA; 10 V source and 2 Ω in branch AB.]

Reading the figure

Triangle ABC with centre O. Branches: C–A = 1 Ω, C–B = 1.5 Ω, C–O = 4 Ω, O–A = 4 Ω, O–B = R (unknown). Between A and B there is a 10 V battery in series with 2 Ω.

This is a Wheatstone bridge: the supply is across A and B, and branch OC is the detector. When the current in OC is zero, V_O = V_C (the bridge is balanced).

Balance condition

R_CA/R_CB = R_OA/R_OB

1/1.5 = 4/R

R = 4 × 1.5/1 = 6 Ω

Current through R

With OC carrying no current, the bridge has two parallel paths between A and B:

  • A to C to B: 1 + 1.5 = 2.5 Ω
  • A to O to B: 4 + 6 = 10 Ω

Bridge resistance = 2.5 × 10/12.5 = 2 Ω

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

Source current I = 10/4 = 2.5 A

Voltage across the bridge V_AB = 2.5 × 2 = 5 V

Current in R (path A–O–B) = 5/10 = 0.5 A

Answer: R = 6 Ω; current through R = 0.5 A

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Basic Electrical Engineering chapter 2 questions →