Question

To what value must you adjust ${\mathbf{R}}_{\mathbf{3}}$to balance a Wheatstone bridge, if the unknown resistancerole="math" localid="1656392044601" ${\mathbf{R}}_{\mathbf{x}}\mathbf{is}\mathbf{}\mathbf{100}\mathbf{}\mathbf{\Omega }\mathbf{,}\mathbf{}{\mathbf{R}}_{\mathbf{1}}\mathbf{}\mathbf{is}\mathbf{}\mathbf{50}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{\Omega }\mathbf{,}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{R}}_{\mathbf{2}}\mathbf{}\mathbf{is}\mathbf{}\mathbf{175}\mathbf{}\mathbf{\Omega }$?

Short answer

The value for the unknown resistance in the Wheatstone bridge is ${\mathrm{R}}_3=28.6\mathrm{\Omega }$.

Step-by-step solution

Concept Introduction

A Wheatstone bridge is an electrical circuit that balances two legs of a bridge circuit, one of which includes the unknown component, to measure an unknown electrical resistance. The circuit's main advantage is its capacity to deliver exceedingly exact readings.

Information Provided

• The Wheatstone bridge with a resistance:${\mathrm{R}}_{\mathrm{x}}=100\mathrm{\Omega }$

• The values for ${\mathrm{R}}_1=50\mathrm{\Omega },{\mathrm{R}}_2=175\mathrm{\Omega }$.

Calculation for Resistance

The formula for calculating the resistance is –

$$\begin{gathered} \frac{{\mathrm{R}}_{\mathrm{x}}}{{\mathrm{R}}_3}=\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1} \\ {\mathrm{R}}_3={\mathrm{R}}_{\mathrm{x}}\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2} \\ {\mathrm{R}}_3=(100\mathrm{\Omega })\times \frac{50\mathrm{\Omega }}{175\mathrm{\Omega }} \\ {\mathrm{R}}_3=28.6\mathrm{\Omega } \end{gathered}$$

Therefore, the value for resistance is ${\mathrm{R}}_3=28.6\mathrm{\Omega }$.