Practical Electronics/WheatStone Network

Intro

A network consist of four resistors connected as shown

The equivalent circuit of the network above

Analysis

$V_{1}={\frac {R_{2}}{R_{2}+R_{1}}}$

$V_{2}={\frac {R_{4}}{R_{4}+R_{3}}}$

• $V_{1}=V_{2}$

${\frac {R_{2}}{R_{2}+R_{1}}}={\frac {R_{4}}{R_{4}+R_{3}}}$

There is no current flow from V₁ to V₂ or from V₂ to V₁

• $V_{1}>V_{2}$

${\frac {R_{2}}{R_{2}+R_{1}}}>{\frac {R_{4}}{R_{4}+R_{3}}}$

There is current flow from V₁ to V₂

• $V_{1}<V_{2}$

${\frac {R_{2}}{R_{2}+R_{1}}}<{\frac {R_{4}}{R_{4}+R_{3}}}$

There is current flow from V₂ to V₁

This network can be used as Controlled Current Voltage Comparator .

• When the two voltage are the same no current flow .
• When there is difference between the two voltages current is non zero and flow in the direction of high voltage to low voltage

This network can be used as Adjust Voltage Zero Current

From V₁ = V₂, I = 0

${\frac {R_{2}}{R_{2}+R_{1}}}={\frac {R_{4}}{R_{4}+R_{3}}}$

R₂ = R₄ provided R₁ + R₂ = R₃ + R₄

This network can be used to turn current to zero by adjusting the value of R₂ equal to the value of R₄ provided that R₁ + R₂ = R₃ + R₄

This network can be used as Resistance Indicator

From ${\frac {R_{2}}{R_{2}+R_{1}}}={\frac {R_{4}}{R_{4}+R_{3}}}$

Hence, $R_{2}=R_{4}{\frac {R_{2}+R_{1}}{R_{4}+R_{3}}}$

Summary

This network can be used as Controlled Current Voltage Comparator , Adjust Voltage Zero Current , Resistance Indicator