Campbell's Modification of Heaviside Bridge

 Campbell's Modification of Heaviside Bridge

fig shows a modified Heaviside bridge. This modification is due to Campbell. This is used to measure self-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 the switch being open and the coil R2, L2 under measurement. Two sets of readings are taken one with the switch being open and the other with the switch being closed. Let values of M and r, Be M1 and R1 with the switch open and M1 and r2 with the switch closed.

we have L2+L = ( M(R3 + R4) + R4.L1 )/R3

and               L = ( M2 ( R3 + R4) + R4.L1)/R3

  Therfore     L2 = (M1 - M2)(1 + R4/R3)

similarly  we can write: R2+R = (R1 + r1).R4/R3  and R = (R1 + R2).R4/R3

                       R2= (r1 - r2).R4/R3

This method is a good example of the method adopted to eliminate the effects of leads etc.

if R3 = R4

            L2 = 2(M1 - M2)

            R2 =  r1 - r2