Question 15.8: Two coils are wound on a toroidal core as illustrated in Fig...
Two coils are wound on a toroidal core as illustrated in Figure 15.16. The reluctance of the core is 10^7 (ampere-turns)/Wb. Determine the self inductances and mutual inductance of the coils. Assume that the flux is confined to the core so that all of the flux links both coils.
The self inductances can be computed using Equation 15.25. For coil 1, we have
L = \frac{N^2}{ \mathcal{R} } (15.25)
L_1 = \frac{N^2_1} {\mathcal{R}}= \frac{100^2} {10^7} = 1 mH
Similarly, for coil 2 we get
L_2 = \frac{N^2_2} {\mathcal{R}}= \frac{200^2} {10^7} = 4 mH
To compute the mutual inductance, we find the flux produced by i_1:
\phi_1 = \frac{N_1i_1} {R} = \frac{100i_1} {10^7} = 10^{−5}i_1
The flux linkages of coil 2 resulting from the current in coil 1 are given by
λ_{21} = N_2\phi_1 = 200 × 10^{−5}i_1
Finally, the mutual inductance is
M = \frac{λ_{21}}{ i_1} = 2 mH