Potential Difference Between Two Points — Question 3

Question 3

Grounding the divider midpoint changes labels but not the current

An ideal 18.0 V source drives a divider with R1=2.00 ohm above midpoint M and R2=4.00 ohm below it. Set VM=0 by choosing M as the reference; ground supplies no additional current.

1. Find the common current and source terminal potentials VA and VB.

2. Find VB-VA and the two resistor drops to show that the reference choice preserves all physical voltages.

Question 3 - Solution

Grounding the divider midpoint changes labels but not the current

(a) Method and calculation

$$I=18/(2+4)=3.00\,\mathrm A.$$$$V_B-V_M=I R_1=6.00\,\mathrm V,\quad V_M-V_A=IR_2=12.0\,\mathrm V.$$

(b) Interpretation and further calculation

$$V_B=+6.00\,\mathrm V,\quad V_A=-12.0\,\mathrm V,\quad V_B-V_A=18.0\,\mathrm V.$$$$V_{R_1}=6.00\,\mathrm V,\quad V_{R_2}=12.0\,\mathrm V.$$

Physical check

A zero reference is not necessarily the lowest potential in a circuit.