1. Calculate the voltage across the resistor immediately after 150 tau\'s have e

Question

1. Calculate the voltage across the resistor immediately after 150 tau's have elapsed.

2. Calculate the current in the circuit after the switch has been closed for 2.3 tau's.

3. Calculate the current in the circuit after the switch has been closed for 250 tau's

Question: An inductor is made by tightly winding a 12.5 m long AwG 2-guage wire around a cardboard cylinder of radius 7.5 cm. This inductor is placed in series with an R 5.5 k2 resistor and connected to a 9.0 V dc battery via a switch. At time t 0.0s, the switch is closed. We will take the following steps to answer a few questions about this circuit.

Explanation / Answer

1)

voltage across resistor at any time t is

v = V_max*(1-e^(-t/T))

V = 9*(1-e^(-150)) = 9 V

2) i =Imax*(1-e^(-t/T))

i = (V/R)*(1-e^(-t/T))

i = (9/5500)*(1-e^(-2.3))

i = 1.47*10^-3 A

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3) i =Imax*(1-e^(-t/T))

i = (V/R)*(1-e^(-t/T))

i = (9/5500)*(1-e^(-250)) = 1.64*10^-3 A

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