Electric Potential — Question 4

Question 4

Reference changes preserve every measurable voltage difference

Three nodes obey $V_B-V_A=20.0$ V and $V_C-V_B=-35.0$ V. Initially assign $V_A=100$ V.

1. Find all three potentials and $V_C-V_A$.

2. Reassign C to zero potential. Find the new node potentials and show that the work moving charge q from A to C is unchanged.

Question 4 - Solution

Reference changes preserve every measurable voltage difference

(a) Method and calculation

$$V_A=100\,\mathrm V,\quad V_B=120\,\mathrm V,\quad V_C=85.0\,\mathrm V.$$$$V_C-V_A=-15.0\,\mathrm V.$$

(b) Interpretation and further calculation

$$V_i\prime=V_i-85.0\,\mathrm V:\quad(V_A\prime,V_B\prime,V_C\prime)=(15.0,35.0,0)\,\mathrm V.$$$$W_e=q(V_A-V_C)=q(V_A\prime-V_C\prime)=q(15.0\,\mathrm V).$$

Physical check

A common additive constant changes assigned energies by q times that constant but cancels from work.