Practical Electronics/WheatStone Network

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Intro

A network consist of four resistors connected as shown

The equivalent circuit of the network above

Analysis

${\displaystyle V_{1}={\frac {R_{2}}{R_{2}+R_{1}}}}$
${\displaystyle V_{2}={\frac {R_{4}}{R_{4}+R_{3}}}}$
• ${\displaystyle V_{1}=V_{2}}$
${\displaystyle {\frac {R_{2}}{R_{2}+R_{1}}}={\frac {R_{4}}{R_{4}+R_{3}}}}$
There is no current flow from V1 to V2 or from V2 to V1
• ${\displaystyle V_{1}>V_{2}}$
${\displaystyle {\frac {R_{2}}{R_{2}+R_{1}}}>{\frac {R_{4}}{R_{4}+R_{3}}}}$
There is current flow from V1 to V2
• ${\displaystyle V_{1}
${\displaystyle {\frac {R_{2}}{R_{2}+R_{1}}}<{\frac {R_{4}}{R_{4}+R_{3}}}}$
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 volatage

This network can be used as Adjust Voltage Zero Current

From V1 = V2, I = 0
${\displaystyle {\frac {R_{2}}{R_{2}+R_{1}}}={\frac {R_{4}}{R_{4}+R_{3}}}}$
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 ${\displaystyle {\frac {R_{2}}{R_{2}+R_{1}}}={\frac {R_{4}}{R_{4}+R_{3}}}}$
Hence, ${\displaystyle R_{2}=R_{4}{\frac {R_{2}+R_{1}}{R_{4}+R_{3}}}}$

Summary

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