# 13.9.1: The Owen Bridge

FIGURE \(\text{XIII.9}\)

This bridge can be used for measuring inductance. Note that the unknown inductance is the only inductance in the bridge. Reactance is supplied by the capacitors.

Equation 13.9.1 in this case becomes

\[\tag{13.9.2}\frac{R_1}{R_2+jL_2\omega}=\frac{-j/(C_3\omega)}{R_4-j/(C_4\omega)}.\]

That is,

\[\tag{13.9.3}R_1R_4-j\frac{R_1}{C_4\omega}=\frac{L_2}{C_3}-j\frac{R_2}{C_3\omega}.\]

On equating real and imaginary parts separately, we obtain

\[\tag{13.9.4}L_2=R_1R_4C_3\]

and

\[\tag{13.9.5}\frac{R_1}{R_2}=\frac{C_4}{C_3}.\]