Two series coils, each with an L of 250 μH, have a total inductance of 550 μH connected series-aiding and 450 μH series-opposing. (a) How much is the mutual inductance LM between the two coils? (b) How much is the coupling coefficient k?

Question

Two series coils, each with an L of 250 [latex]\mu [/latex] H, have a total inductance of 550[latex]\mu [/latex]H connected series-aiding and 450 [latex]\mu [/latex]H series-opposing. (a) How much is the mutual inductance [latex]L_M[/latex] between the two coils? (b) How much is the coupling coefficient k?

Accepted Answer

a. [latex]L_M=\frac{L_{T_a}-L_{T_o}}{4} [/latex]

[latex]=\frac{550-450}{4}=\frac{100}{4}[/latex]

[latex]= 25 \mu H[/latex]

b. [latex]L_M=k\sqrt{L_1L_2}, [/latex] or

[latex]k=\frac{L_M}{\sqrt{L_1L_2}}=\frac{25}{\sqrt{250 imes 250}}[/latex]

[latex] =\frac{25}{250}=\frac{1}{10}[/latex]

=0.1

Question 18.20: Two series coils, each with an L of 250 μH, have a total ind...

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