This bridge measures mutual inductance in terms of known self- Inductance.
Figure 1 shows a modified Heaviside Bridge. This modification is due to Campbell. This is used to measure a self inductance in terms of a mutual Inductance. In this case an additional balancing coil L, R, is included in arm ad in series with inductor under test. An additional resistance r is put in arm ab. Balance is obtained by varying M and r. A short circuiting switch is placed across the coil R2, L2 under measurement. Two sets of readings are taken one with switch (K) being open and other switch being closed. Let values of M and r, be M1 and r1 with switch open, and M2 and r2 with switch closed.
Applying voltage across abc is equal to voltage across adc.
Switch (K) open
and with Switch(K) closed
This is a good example of the methods adopted to eliminate the effects of leads etc.