Consider the following bridge circuit where R4 is unknown and needs to be determined.
(1) Determine the value of R4 so that the bridge circuit becomes balanced.
(2) Writing down the expression for the reading of detector voltage Vo in terms of circuit components values (Vb, R1, R2, R3, and R4)
a. What will happen to the detector voltage if the power supply voltage increases?
b. Analyze this expression and determine the value of R4 so that detector voltage being 0.03V.

See explanations

Explanation:

(a) Assuming R3 is set such that the bridge is balanced (i.e. Vab = 0), derive an analytical expression for

Rx in terms of R1, R2 and R3.

Since Vab = 0, Va and Vb must be equal. Using voltage divider relations gives:

Va = Vin µ

R3

R1 + R3

¶

and Vb = Vin µ

Rx

R2 + Rx

¶

Setting these equal to each other and simplifying, we get

R1

R3

=

R2

Rx

, or Rx =

R2R3

R1

.

(b) . . . suppose that Rx varies in a way that makes Vab nonzero. Derive an expression for the dependence

of Vab on Rx.

Vab = Vb−Va = Vin µ

Rx

R2 + Rx

−

R3

R1 + R3

¶

or, if you prefer: Vab = Vin ·

R1Rx − R2R3

(R1 + R3)(R2 + Rx)

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