Potential Difference Between Two Points — Question 2

Question 2

Two paths around a steady loop give the same endpoint voltage

An ideal 18.0 V source connects A to B with B positive. A 4.00 ohm resistor connects B to C; ideal wire connects C to D; a 2.00 ohm resistor connects D to A.

1. Find the loop current and VC-VA along A-B-C.

2. Find the same difference along A-D-C and explain what a disagreement would imply.

Question 2 - Solution

Two paths around a steady loop give the same endpoint voltage

(a) Method and calculation

$$I=18.0/(4+2)=3.00\,\mathrm A.$$$$V_C-V_A=(V_B-V_A)+(V_C-V_B)=18-3(4)=6.00\,\mathrm V.$$

(b) Interpretation and further calculation

$$V_D-V_A=+I(2)=6.00\,\mathrm V,\quad V_C-V_D=0.$$$$V_C-V_A=6.00+0=6.00\,\mathrm V.$$A different result would signal inconsistent signs or data within the stationary lumped-circuit model.

Physical check

A resistor is a potential rise when traversed against the actual current direction.