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A coil of some internal resistance 'r' b...

A coil of some internal resistance `'r'` behaves line an inductance. When it is connected in series with a resistance `R_(1)`, the time constant is found to be `tau_(1)`. When it is connected in series with a resistance `R_(2)`, the time constant is found to be `tau_(2)`. The inductance of the coil is

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