Owens Bridge

This bridge is used to measure the inductance of a coil in terms of resistance and capacitance. C₁ and C₂ are standard capacitors. R₁ and R₃ are variable resistances. R₄ is a fixed resistance. The coil whose self-inductance L is to be determined is connected in the arm AD in series with R₃.

Let the impedances in the four arms of the bridge be Z₁, Z₂, Z₃, and Z₄ at the balance points.
    Z₁ = R₁ + 1/jC₁ω; Z₂ = 1/jC2ω; Z₃ = R₃ + JLω; Z₄ = R₄

When the bridge is balanced, we have
    Z₁/Z₂ = Z₃/Z₄
Or    Z₁Z₄ = Z₂Z₃
    (R1 + I/jC₁ω)R₄ = I/jC₂ω - (R₃ + jLω)
    R₁R₄ + R₄/jC₁ω = R₃/jC₂ω + L/C₂

Equating the imaginary Parts, we have

    R₄/R₁ = R₃/C₂ or R₃/R₄ = C₂/C₁                            … (1)

Equating the real parts, R1R4 = L/C₂
. :            L = R₁R₄C₂                             … (2)

Thus we have two balances conditions which are independent of one another. The condition (1) is satisfied by varying R₃ and (2) by varying R₁ till the sound is minimum in both the cases.



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