First slide
Time -Varying current in L-R circuit
Question

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?

Moderate
Solution

i=io1eR2tdidt=ioR2eR2tLdidt=ioReR2t=ioR2eR2t=21eR2t=2ln2=RLtt=LRln2=τln2

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