The time constant of an inductance coil is $2 .0 \times 10^{- 3} s$ . When a $90 Ω$ resistance is joined in series, then the time constant becomes $0.5 \times 10^{- 3} s$ . The inductance and resistance of the coil are

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$60 mH, 60 Ω$

$60 mH, 30 Ω$

$30 mH, 30 Ω$

$30 mH, 60 Ω$

answer is C.

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Detailed Solution

Time constant, $τ = \frac{L}{R} = 2 .0 \times 10^{- 3} s and \frac{L}{R + 90} = 0 .5 \times 10^{- 3} s$
Solving these two equations, we get L=60mH and R=30 $Ω$

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