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Mutual Inductance measurement by Heaviside Bridge
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This bridge (Fig.1) measures mutual inductance in terms of a known self-inductance. The same bridge, slightly modified, was used by Campbell to measure a self-inductance in terms of known mutual inductance.

                                           Fig. 1. Heaviside mutual inductance bridge

Let , M= unknown mutual Inductance ,

L1= self-inductance of secondary of mutual inductance ,

L2= known self-inductance  ,

R1, R2, R3, R4= non inductive resistors,

At balance voltage drop between b and c must equal the voltage drop between d and c. Also the votage drop across a-b-c must equal the voltage drop across a-d-c. Thus we have the following equations at balance.

I_1R_3=I_2R_4

and, (I_1+I_2)jwM+I_1(R_1+R_3+jwL_1)=I_2(R_2+R_4+jwL_2)

..\dpi{100} \fn_jvn (I_1+I_2)jwM+I_1(R_1+R_3+jwL_1)=I_2(R_2+R_4+jwL_2)\\ \therefore I_2(\frac{R_4}{R_3}+1)jwM+I_2\frac{R_4}{R_3 }(R_1+R_3+jwL_1)=I_2(R_2+R_4+jwL_2)\\ or, (\frac{R_4}{R_3}+1)jwM+\frac{R_4}{R_3 }(R_1+R_3+jwL_1)=(R_2+R_4+jwL_2)\\

Thus,

 R_1=\frac{R_2}{R_3}{R_4} ..................................... (1)

and,

M=\frac{L_2-L_1\frac{R_4}{R_3}}{\frac{R_4}{R_3}+1}

\therefore M=\frac{R_3L_2-R_4L_1}{R_3+R_4} ......................(2)

It is clear from Eqn. (2), that L1, the self inductance of the secondary of the mutual inductor must be known in order that M be measured by this method.

In case, R3=R4, we get, 

M=\frac{L_2-L_1}{2} ..............(3)\\ and, R_1=R_2......................(4)

 This method can be used for measurement of self-inductance. 

 

 

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