---
title: "Find R when branch DA current is zero"
subject: "Basic Electrical Engineering"
chapter: 2
key: "semester_1/basic_electrical_engineering:find-r-current-branch-da-zero"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/find-r-current-branch-da-zero
site: BCT Engineering
---

# Find R when branch DA current is zero

Basic Electrical Engineering · Chapter 2: DC circuits

- Asked in: 2069 Chaitra, 4 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/find-r-current-branch-da-zero
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-2

## Question

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.]

## 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.

## Answer

#### 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**

## Check yourself

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

1. If DA carries zero current,
   A. R is infinite
   B. DA is shorted
   C. the source is zero
   D. V_D = V_A and its resistance is not needed
   Answer: D. A balanced bridge ignores the detector branch. (Key point: Detector branch)

2. The condition 2/2 = 2/R gives
   A. R = 4 Ω
   B. R = 1 Ω
   C. R = 2 Ω
   D. R = 0.5 Ω
   Answer: C. Ratio of arms equal. (Key point: Balance)

3. Bridge resistance 2 Ω + 2 Ω series gives I = 5 A; the current in R is
   A. 5 A
   B. 10/(2 + 2) = 2.5 A
   C. 10/2 = 5 A
   D. 1.25 A
   Answer: B. Bridge voltage is 10 V across the path B-D-C of 4 Ω. (Key point: Current in R)

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