Potential Difference Between Two Points — Question 7

Question 7

A bridge balance is equality of two divider potentials

Between nodes A and B, held at VA=9.00 V and VB=0, the upper series path has resistors 3.00 ohm from A to M and 6.00 ohm from M to B. The lower path has 2.00 ohm from A to N and unknown X from N to B. No wire joins M and N.

1. Find X such that VM=VN.

2. Find branch currents at balance and explain what an ideal zero-current detector connected between M and N would read.

Question 7 - Solution

A bridge balance is equality of two divider potentials

(a) Method and calculation

$$V_M=9\frac6{3+6}=6.00\,\mathrm V,\quad V_N=9\frac X{2+X}.$$$$6=9X/(2+X)\Rightarrow X=4.00\,\Omega.$$

(b) Interpretation and further calculation

$$I_{\mathrm{upper}}=9/(3+6)=1.00\,\mathrm A,\quad I_{\mathrm{lower}}=9/(2+4)=1.50\,\mathrm A.$$$$V_M-V_N=0\Rightarrow I_{\mathrm{detector}}=0.$$

Physical check

Zero voltage between two nodes does not require zero current in the separate paths feeding them.