Multiloop Circuits — Question 4

Question 4

An unbalanced resistive bridge requires coupled node equations

A bridge is held at VA=10.0 V and VB=0. Resistances A-M, M-B, A-N and M-N are each 1.00 ohm; N-B is 2.00 ohm.

1. Solve for VM and VN and give the signed cross-branch current from M to N.

2. Find the total source current and power; explain why neither middle node can be treated as an isolated divider.

Question 4 - Solution

An unbalanced resistive bridge requires coupled node equations

(a) Method and calculation

$$(V_M-10)+V_M+(V_M-V_N)=0,\quad(V_N-10)+V_N/2+(V_N-V_M)=0.$$$$V_M=70/13\,\mathrm V,\quad V_N=80/13\,\mathrm V,\quad I_{MN}=-10/13\,\mathrm A.$$

(b) Interpretation and further calculation

$$I_s=(10-V_M)+(10-V_N)=110/13\,\mathrm A.$$$$P_s=10I_s=1100/13\,\mathrm W\simeq84.6\,\mathrm W.$$The nonzero cross current loads both dividers.

Physical check

The cross current flows from N to M, consistent with the solved potentials.