Electrical Engineering ⇒ Topic : General Equation for Bridge Balance
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Seema
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GENERAL EQUATION FOR BRIDGE BALANCE The balance condition of the bridge requires that there should not be any current through the detector. If the potential difference between a and b is equal to that of a and d in magnitude and phase, there will be no current through the detector D. [See Figure (a)] FIGURE (a) V1 = V2 ...........(1) I1Z1 = I2Z2 ............... (2) Using Eqs. (3) and (4), Eq. (2) can be written as: Z1Z4 = Z2 Z3 .........(5) Let Z1 = |Z1| ∠θ1, Z2 = |Z2| ∠θ2, Z3 = |Z3|, ∠θ3,and Z4 = |Z4| ∠θ4 in terms of polar coordinates. Therefore, Eq. (5) becomes | Z1|∠θ1 |Z4| ∠θ4 = |Z2| ∠θ2 |Z3| ∠θ3 |Z1| |Z4| = |Z2| |Z3| ...........(6) and ∠(θ1 + θ4) = ∠(θ2 + θ3) ............. (7) Now, Eq. (5) becomes Equating real and imaginary parts, it can be written as:
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