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Self Inductance measurement of an unknown coil by Heaviside Campbell Equal Ratio Bridge
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Figure 1 shows Heaviside Campbell equal ratio  bridge. This is a better arrangement which improves sensitivity and also dispenses with the use of a balancing coil.

                Fig. 1. Heaviside Campbell equal ratio bridge.

In this method, the secondary of a mutual inductor is made up of two equals coils each having a self inductance. One of the coils is connected in arm ab and other in arm ad. The primary of mutual inductance reacts with both of them. L2, R2, is the coil whose self inductance and resistance is to be determined. The resistances R3, R4 are made equal. Balance is obtained by varying the mutual inductance and resistance r.

At balance, 

I_1R_3=I_2R_4\\ but, R_3=R_4\\ and \therefore I_1=I_2=I/2\\ as I=I_1+I_2.

writing the other equation for balance:

\dpi{100} \fn_jvn I_1(R_1+r)+I_1jwL+IjwM_x=I_2R_2+I_2jw(L_2+L)-IjwM_y\\ or, \frac{R_1+r}{2}+jw(\frac{L}{2}+M_x)=\frac{R_2}{2}+jw(\frac{L_2+L}{2})-jwM_y

Equating the real and imaginary terms,

R2=R1+r......................................(1)

L2=2(Mx+My)=2M......................(2)

Thus the magnitude of inductance which can be measured with this method is twice the range of the mutual inductor.

 

 

 

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