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When a coil joined to a cell, the curren...

When a coil joined to a cell, the current through the coil grows with a time constant `tau`. After what time, the current will reach 10% of its steady- state value?

Text Solution

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Given by `i=i_0 (1-e^(t/tau)), (i_0)/(10) = i_0 (1-e^(t/tau)) , 9/10 = e^(-t/tau)`
`10/9 = e^(t/tau) ` , applying log on both sides
`ln(10/9) = t/tau , t = tau ln (10/9)`
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