A circuit consists of a coil, a switch, and a battery, all in series. The intern

Question

A circuit consists of a coil, a switch, and a battery, all in series. The internal resistance of the battery is negligible compared with that of the coil. The switch is originally open. It is thrown closed, and after a time interval ?t, the current in the circuit reaches 85.8% of its final value. The switch then remains closed for a time interval much longer than ?t. The wires connected to the terminals of the battery are then short-circuited with another wire and removed from the battery, so that the current is uninterrupted.

(a) At an instant that is a time interval ?t after the short circuit, the current is what percentage of its maximum value?
%

(b) At the moment 2?t after the coil is short-circuited, the current in the coil is what percentage of its maximum value?
%

Explanation / Answer

For a inductor,

i = io* (1 - e^(-t/T)) , where io is the max current, t is time and T is time constant for the circuit.

Now, it's given than for t = delta_t , i/io = 0.858

Therefore, T = delta_t / 1.952

a) For decay, i = io * e^(-t/T)

or, i/io = 0.142 or the current is 14.2% of its max value.

b) for t = 2*delta_t

i/io = 0.02 or the current is 2% of its max value

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