Question

When an unknown resistance${\mathbf{R}}_{\mathbf{x}}$is placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting ${\mathbf{R}}_{\mathbf{3}}$to be $\mathbf{2500}\mathbf{\Omega }$. What is ${\mathbf{R}}_{\mathbf{x}}$if$\frac{{\mathbf{R}}_{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{1}}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{625}$?

Short answer

The value for the unknown resistance in the Wheatstone bridge is ${\mathrm{R}}_{\mathrm{x}}=1562.5\mathrm{\Omega }$.

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:$R_3=2500\Omega$
• The values for $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}=0.625.$.

Calculation for Resistance

The formula for calculating the resistance is –

$$\begin{gathered} {\mathrm{R}}_{\mathrm{x}}={\mathrm{R}}_3\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1} \\ =(2500\mathrm{\Omega })\times 0.625 \\ =1562.5\mathrm{\Omega } \end{gathered}$$

Therefore, the value for resistance is ${\mathrm{R}}_{\mathrm{x}}=1562.5\mathrm{\Omega }$.