Q.

At t =0, an inductor of zero resistance is joined to a cell of emf  through a resistance. The current increases with a time constant τ . After what time will the potential difference across the coil be equal to that across the resistance?

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a

T

b

T 1n 2

c

T (1-ln2)

d

T /1n2

answer is B.

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Detailed Solution

i=io1−e−R2tdidt=ioR2e−R2tLdidt=ioRe−R2t=ioR2e−R2t=2−1eR2t=2ln2=RLtt=LRln2=τln2
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At t =0, an inductor of zero resistance is joined to a cell of emf  through a resistance. The current increases with a time constant τ . After what time will the potential difference across the coil be equal to that across the resistance?