A 320 H coil is in series with a 3.3 k resistor. How long does it take for current to build up to its full value?

ANS:C - 0.48 s

TIME CONSTANT AND CURRENT RELATIONSHIP:

0 0% of max current.
1Ts 63.2% of max current.
2Ts 86.5% of max current.
3Ts 95% of max current.
4Ts 98.2% of max current.
5Ts 100% of max current.

So, first we know that the maximum possible current through the circuit will be full, means the 100% of max current and the time constant will be 5Ts so,

Time constant => T= (L/R) = (320u/3.3k).
When it reaches max current(100%) it will take 5Ts.
So 5Ts = 5(320u/3.3k),
=0.48us.