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Chapter 30: Q47P (page 899)

Inductors in series. Two inductors L1 and L2 are connected in series and are separated by a large distance so that the magnetic field of one cannot affect the other.(a)Show that the equivalent inductance is given by

Leq=L1+L2

(Hint: Review the derivations for resistors in series and capacitors in series. Which is similar here?) (b) What is the generalization of (a) for N inductors in series?

Short Answer

Expert verified

a)Leq=L1+L2

b)Leq=鈭�n=1nLn

Step by step solution

01

Given

i) L1- Inductance of inductor 1.

ii) L2- Inductance of inductor 2.

iii) Leq- Equivalent inductance of series connection.

iv) Hint: Review the derivation for resistors in series and capacitors in series.

02

Understanding the concept

Net voltage across the series connection of inductors is the sum of voltages across each inductor.

Formulae:

Net voltage for series connection of inductors:

V=V1+V2V1-voltageacrossL1V2-voltageacrossL2

03

Show that the equivalent inductance is given by Leq=L1+L2

For series connection, the current is the same for each inductor.

V=V1+V2LeqI=L1I+L2I

Hence,

Leq=L1+L2

04

(b) Find the generalization of (a) for   conductors in series

Equivalent inductance fornumbers of inductors in series is

Leq=L1+L2+L3+鈰�+Ln

Generalization oftheabove formula is

Leq=鈭�n=1nLn

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