Skip to main content

Find Vxy in circuit

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).

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.]

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).

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Basic Electrical Engineering chapter 2 questions →