---
title: "Unknown R when branch OC current zero"
subject: "Basic Electrical Engineering"
chapter: 2
key: "semester_1/basic_electrical_engineering:unknown-resistance-r-branch-oc-zero"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/unknown-resistance-r-branch-oc-zero
site: BCT Engineering
---

# Unknown R when branch OC current zero

Basic Electrical Engineering · Chapter 2: DC circuits

- Asked in: 2070 Chaitra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/unknown-resistance-r-branch-oc-zero
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-2

## Question

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.]

## 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.

## Answer

#### 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**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. If the current in OC is zero then
   A. V_O = 0
   B. the source is off
   C. R = 0
   D. V_O = V_C, so the bridge is balanced
   Answer: D. No current in the detector branch means equal potentials at both ends. (Key point: Balance meaning)

2. The balance condition 1/1.5 = 4/R gives
   A. R = 2.67 Ω
   B. R = 1.5 Ω
   C. R = 6 Ω
   D. R = 4 Ω
   Answer: C. R = 4 x 1.5/1 = 6 Ω. (Key point: Value of R)

3. The A-C-B path (2.5 Ω) and A-O-B path (10 Ω) are in parallel, giving
   A. 12.5 Ω
   B. 2 Ω
   C. 4 Ω
   D. 25 Ω
   Answer: B. 2.5 x 10/12.5 = 2 Ω. (Key point: Bridge resistance)

4. With V_AB = 5 V, the current through R is
   A. 5/10 = 0.5 A
   B. 5/6 A
   C. 2.5 A
   D. 5 A
   Answer: A. The path A-O-B has 4 + 6 = 10 Ω, so I = 5/10 = 0.5 A. (Key point: Current in R)

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