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Solved: Two coils are wrapped around each other as shown
Chapter 30, Problem 78CP(choose chapter or problem)
Two coils are wrapped around each other as shown in Fig. 30.3. The current travels in the same sense around each coil. One coil has self-inductance \(L_{1}\), and the other coil has self-inductance \(L_{2}\). The mutual inductance of the two coils is M. (a) Show that if the two coils are connected in series, the equivalent inductance of the combination is \(L_{e q}=L_{1}+L_{2}+2 M\). (b) Show that if the two coils are connected in parallel, the equivalent inductance of the combination is
\(L_{\mathrm{eq}}=\frac{L_{1} L_{2}-M^{2}}{L_{1}+L_{2}-2 M}\)
Equation Transcription:
Text Transcription:
L_1
L_2
L_eq=L_1+L_2+2M
L_eq=L_1L_2-M^2 over L_1+L_2-2M
Questions & Answers
QUESTION:
Two coils are wrapped around each other as shown in Fig. 30.3. The current travels in the same sense around each coil. One coil has self-inductance \(L_{1}\), and the other coil has self-inductance \(L_{2}\). The mutual inductance of the two coils is M. (a) Show that if the two coils are connected in series, the equivalent inductance of the combination is \(L_{e q}=L_{1}+L_{2}+2 M\). (b) Show that if the two coils are connected in parallel, the equivalent inductance of the combination is
\(L_{\mathrm{eq}}=\frac{L_{1} L_{2}-M^{2}}{L_{1}+L_{2}-2 M}\)
Equation Transcription:
Text Transcription:
L_1
L_2
L_eq=L_1+L_2+2M
L_eq=L_1L_2-M^2 over L_1+L_2-2M
ANSWER:
Problem 78CP
Solution 78 CP
Step 1 :
Introduction
In this question, we need to show if two coils are connected in series, equivalent inductance is given by
In the second part we need to show if the coils are connected in parallel combination, the equivalent inductance is given by
Considering given figure