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# The time constant of inductance coil is 3 m sec. When a $90\;\Omega$ resistance is joined in series, then the time constant becomes 0.5 m sec. The inductance and the resistance of the coil are :

$\begin {array} {1 1} (1)\;54\;mH,\;18\; \Omega & \quad (2)\;14\;mH,\;42\; \Omega \\ (3)\;42 \;mH,\;14\; \Omega & \quad (4)\;14\;mH,\;60\; \Omega \end {array}$

$(1)\;54\;mH,\;18\; \Omega$