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Question

# Two inductances L1 and L2 are connected in series and are separated by a large distance:(i) Show that their equivalent inductance is L1+L2.(ii) Why must their separation be large?

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Solution

## ( i )To prove that equivalent inductance [in series] is L1 and L2Let a common current I be flowing, in the circuit, passing through L1 and L2.i.e. I=IL1+IL2 (1)According to Kirchhoff's Voltage Law,V=VL1+VL2 (2)Also, we know thatV=LdidtPutting in equation (2)Ldidt=L1didt+L2didt (3) [since, I is same across AB]Dividing the above equation by didt both sidesL=L1+L2.( ii )When two or more coils are magnetically linked together by a common magnetic flux, they are said to have a property of mutual induction. This mutual inductance can be a negative thing, as leakage inductance from coil can interfere with the operation of other adjacent components.Thus the separation should be large.

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