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Question

A uniformly wound long solenoid of inductance L and resistance R is cut into two parts in the ratio η:1, which are then connected in parallel. The combination is then connected to a cell of emf E. The time constant of the circuit is :

A
LR
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B
L(η+1)R
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C
(ηη+1)LR
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D
(η+1η)LR
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Solution

The correct option is A LR
L1=(ηη+1)L,R1=(ηη+1)R
L2=(1η+1)L,R2=(1η+1)R
Lnet=L1L2L1+L2=ηLL(η+1)(ηL+L)
Similarly, Rnet=R1R2R1+R2=ηRR(η+1)(ηR+R)
τL=LnetRnet=LR

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