---
title: "Find Vxy in circuit"
subject: "Basic Electrical Engineering"
chapter: 2
key: "semester_1/basic_electrical_engineering:find-vxy-2v-8v-3v-6v"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/find-vxy-2v-8v-3v-6v
site: BCT Engineering
---

# Find Vxy in circuit

Basic Electrical Engineering · Chapter 2: DC circuits

- Asked in: 2074 Chaitra, 6 marks
- Video: [Calculate voltage between terminal X and Y](https://www.youtube.com/watch?v=dJU6wXKv_8w) — Engg-Course-Made-Easy
- 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-vxy-2v-8v-3v-6v
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-2

## Question

Find Vxy in the following circuit diagram. [Figure: terminals x and y; 2 V source, 4 Ω and 3 Ω resistors on the left; 3 V source in the middle; 8 V source above a 5 Ω and 3 Ω pair of resistors; 6 V source at the bottom right.]

## Short answer

No current flows in the 3 V source; solve left loop (I = 0.2857 A) and right loop (I = 0.25 A) independently. Combining potentials gives Vxy = Vx−Vy ≈ −0.89 V (y is 0.89 V higher than x).

## Answer

#### Reading the figure
The circuit has two separate closed loops joined only by the 3 V source, so no current flows in the 3 V source and it only adds its voltage.

- Left loop: 2 V (+ on top), 4 Ω, point x, 3 Ω, bottom node P.
- Right loop: node Q, 8 V (+ at Q side), 3 Ω, 6 V (+ at y side), point y, 5 Ω.
- Link: 3 V source from P to Q (+ at Q). Polarities are read from the plate lengths in the figure.

#### Left loop
I = 2/(4 + 3) = 0.2857 A
V_x − V_P = 0.2857 × 3 = 0.857 V

#### Right loop
Net EMF = 8 − 6 = 2 V (the 8 V source drives the current), total R = 5 + 3 = 8 Ω
I = 2/8 = 0.25 A, flowing from Q through the 5 Ω to y
V_Q − V_y = 0.25 × 5 = 1.25 V

#### Combine
V_Q − V_P = +3 V (3 V source)

V_xy = (V_x − V_P) − (V_Q − V_P) + (V_Q − V_y)
V_xy = 0.857 − 3 + 1.25 = −0.893 V

**Answer: V_xy ≈ −0.89 V (point y is 0.89 V higher than x)**

Assumption: battery polarities are taken from the plate lengths in the figure (longer plate = positive).

## Check yourself

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

1. Why does no current flow in the 3 V source?
   A. It is shorted
   B. It links two otherwise separate loops, so there is no closed path through it
   C. It has infinite resistance
   D. It is ideal
   Answer: B. The loops are joined only through the 3 V source, so it has no return path and just adds its voltage. (Key point: Isolated loops)

2. In the left loop (2 V, 4 ohm, 3 ohm) the voltage from x to P is:
   A. 2 V
   B. 0.857 V
   C. 1.143 V
   D. 0.2857 V
   Answer: B. I = 2/7 = 0.2857 A; the 3 ohm drops 0.2857 x 3 = 0.857 V. (Key point: Left loop)

3. The right-loop current, with 8 V and 6 V opposing and total 8 ohm, is:
   A. 14/8 = 1.75 A
   B. 2/8 = 0.25 A
   C. 8/8 = 1 A
   D. 6/8 = 0.75 A
   Answer: B. Net EMF = 8 - 6 = 2 V, so I = 2/8 = 0.25 A, and the 5 ohm drops 1.25 V. (Key point: Right loop)

4. Combining 0.857 V, the 3 V source and 1.25 V gives V_xy of:
   A. +5.1 V
   B. -0.89 V
   C. +0.89 V
   D. -3 V
   Answer: B. V_xy = 0.857 - 3 + 1.25 = -0.893 V. (Key point: Final voltage)

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