Theory
The theory of Owen’s
bridge states that the unknown inductance `L_1` is compared with the known capacitor `C_4` connected to
the arms of the bridge circuit. In the balanced condition, the non-inductive resistor `R_2` and the
variable standard capacitor `C_2` can be varied independently. Hence, no current flows through the bridge
circuit and no potential will be recorded by the null detector.
From Owen’s bridge circuit, we can observe:
- Unknown self-inductance `L_1`
- Pure resistor `R_3` (fixed non-inductive resistance)
- Fixed standard capacitor `C_4`
- Variable non-inductive resistor `R_2` in series with a variable standard capacitor `C_2`.
- A null detector is connected to determine the balance condition of the bridge circuit.
Consider the balanced equation of a basic AC bridge circuit:`Z_1Z_4=Z_2Z_3`
Now, substitute the impedances of Owen’s bridge circuit in the above equation, then:
`((R_1+jωL_1)(1/jωC_4) = (R_2+1/jωC_2)R_3)`
Now, separate the real and imaginary terms from the above equation. We get:
`(L_1=R_2R_3C_4)`
The unknown inductance can be measured from the above equation:
`(R_1= R_3 left(frac(C_4)(C_2)right))`
The value of a variable standard capacitor `C_2` is measured.
From Owen’s bridge circuit, we can observe:
- Unknown self-inductance `L_1`
- Pure resistor `R_3` (fixed non-inductive resistance)
- Fixed standard capacitor `C_4`
- Variable non-inductive resistor `R_2` in series with a variable standard capacitor `C_2`.
- A null detector is connected to determine the balance condition of the bridge circuit.
Consider the balanced equation of a basic AC bridge circuit:
Now, substitute the impedances of Owen’s bridge circuit in the above equation, then:
Now, separate the real and imaginary terms from the above equation. We get:
The unknown inductance can be measured from the above equation:
The value of a variable standard capacitor `C_2` is measured.