After the switch is closed, thecurrentin the circuit grows over time approaching a constant value.Ingeneral, at time t after a voltage source is connected to anL-Rcircuit, the current I(t) in the circuit is given bytheexpression
I(t)=V/R(1-e-t/Ï)
where V is the voltage provided bythebattery, R is the resistance of the resistor, and Ï is thetimeconstant characteristic of the circuit.
What is the current I(Ï) flowing inthecircuit shown in the figure at one time constant after t =0?
Express your answer in amperes.
Hint: To find the current inthecircuit after one time constant, use the expression forI(t)given in the problem, with t equal to Ï. Do not try todeterminethe time constant for this circuit. You would not be ableto do sobecause the inductance L is unknown. Instead, afterplugging in thenumerical values for V and R appropriatefor this circuit andsubstituting Ï for time, simplifyyour expression to get a numericalvalue for the current.