Resonance Bridge for Measurement of Inductance or Capacitance:

One arm of this Resonance Bridge, shown in Fig. 11.29, consists of a series resonance circuit. The series resonance circuit is formed by R_d, C_d and L_d in series. All the other arms consist of resistors only.

Using the equation for balance, we have Z₁Z₄ = Z₂Z₃,

where Z₁ = R_b, Z₂ = R_c, Z₃ = R_a, and Z₄ = R_d + jωL_d – j/ωC_d.

Therefore

Equating the real and imaginary terms

we get

Therefore

Therefore

The Resonance Bridge can be used to measure unknown inductances or capacitances. The losses R_d can be determined by keeping a fixed ratio R_a/R_b and using a standard variable resistance to obtain balance. If an inductance is being measured, a standard capacitor is varied until balance is obtained. If a capaci­tance is being measured, a standard inductor is varied until balance is ob­tained.The operating frequency of the generator must be known in order to cal­culate the unknown quantity. Balance is indicated by the minimisation of sound in the headphones.