It ask's to calculate the time take for the circuit to reach maximum current when the switch is in position 2. I have figured out the maximum current to be 2A but can't seem to get the time.
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True.While five time constants (5T) is a common rule of thumb for assuming that, from a practical standpoint, a circuit has reached steady state, there is nothing magic about it. In a first order circuit such as this, it will have reached 99.3% of its final value. But at 6T it will have reached 99.8%. Depending on the point behind the question, using the 5T rule might be enough, or the point might be to see if you recognize that, in theory, the circuit never reaches the full 2A but, mathematically, only approaches it asymptotically as time grows toward infinity.
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