GATE 2023 IN – Question 54
Four strain gauges $R_A,R_B,R_C,R_D$, each nominally $R$, form the bridge shown. Under force, $R_A,R_D$ increase by $\Delta R$ and $R_B,R_C$ decrease by $\Delta R$. The potentiometer has total resistance $R_v$. For $R=100$ Ω and $\Delta R=1$ Ω, the minimum $R_v$ needed to balance the bridge is ______ Ω (two decimal places).
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Correct answer: 4.00 to 4.10
Explanation
Let the potentiometer portions be $x$ and $R_v-x$. Bridge balance gives $101/(99+x)=99/(101+R_v-x)$, or $200x=400+101R_v$. Since $x\le R_v$, $R_v\ge400/99=4.0404$ Ω. Equality occurs at an end position. Minimum: **4.04 Ω**.