What is a wheat stone bridge ?

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Solution

A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.

Wheatstone Bridge Circuit

By replacing $R_{4}$ above with a resistance of known or unknown value in the sensing arm of the Wheatstone bridge corresponding to $R_{X}$ and adjusting the opposing resistor, $R_{3}$ to “balance” the bridge network, will result in a zero voltage output. Then we can see that balance occurs when:
$\frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{X}} = 1 (B a l a n c e d)$
The Wheatstone Bridge equation required to give the value of the unknown resistance, $R_{X}$ at balance is given as:
$V_{O U T} = (V_{C} - V_{D}) = (V_{R 2} - V_{R 4}) = 0 R_{C} = \frac{R_{2}}{R_{1} + R_{2}} a n d R_{D} = \frac{R_{4}}{R_{3} + R_{4}} A t b a l a n c e : R_{C} = R_{D} S o, \frac{R_{2}}{R_{1} + R_{2}} = \frac{R_{4}}{R_{3} + R_{4}} ∴ R_{2} (R_{3} + R_{4}) = R_{4} (R_{1} + R_{2}) R_{2} R_{3} + / R_{2} R_{4} = R_{1} + R_{4} / R_{1} R_{4} ∴ R_{4} = \frac{R_{2} R_{3}}{R_{1}} = R_{X}$
Where resistors, $R_{1} a n d R_{2}$ are known or preset
values.

Wheatstone Bridge Example No1
The following unbalanced Wheatstone Bridge is constructed. Calculate the output voltage across points C and D and the value of resistor $R_4$ required to balance the bridge circuit.

For the first series arm, ACB
$V_{C} = \frac{R_{2}}{(R_{1} + R_{2})} \times V_{S} V_{C} = \frac{120 Ω}{80 Ω + 120 Ω} \times = 60 v o l t s$
For the second series arm, ADB
$V_{D} = \frac{R_{4}}{(R_{3} + R_{4})} \times V_{S} V_{D} = \frac{160 Ω}{480 Ω + 160 Ω} \times = 100 = 25 v o l t s$
The voltage across points C-D is given as:
$V_{O U T} = V_{C} - V_{D} ∴ V_{O U T} = 60 - 25 = 35 v o l t s$
The value of resistor, R4 required to balance the bridge is given as:
$R_{4} = \frac{R_{2} R_{3}}{R_{1}} = \frac{120 Ω \times 480 Ω}{80 Ω} = 720 Ω$
We have seen above that the Wheatstone Bridge has two input terminals (A-B) and two output terminals (C-D). When the bridge is balanced, the voltage across the output terminals is 0 volts. When the bridge is unbalanced, however, the output voltage may be either positive or negative depending upon the direction of unbalance.

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