i) If the switch is switched to position “a” at t = 0, at what time will the cur

Question

i) If the switch is switched to position “a” at t = 0, at what time will the current through the inductor reach 95% of its final value?

ii) With the switch remaining in position “a,” what is the current through the inductor after a long, long time?

The switch has been in position “a” for a long time. Immediately after the switch is moved from position “a” to position “b”,

iii) What is the initial current through the inductor?

iv) What is the initial voltage across the inductor?

v) How long does it take the current through the inductor to decay to 1/e (~37%) of the value given in part (iii) above?

Explanation / Answer

tau=L/R=0.002/100=0.00002 s 1 time constant--->for 95% 3 time constants (1-1/e^3)*100=95% are needed i "forced response"=V/R=10/100=0.1 A=Io i "natural response"=-Io*e^(-R/L*t) after a long time i=Io the current through the inductor can not change instantaneously thus the current will be Io voltage across the inductor will change instantaneously vL=L*di/dt---> 0.002 di/dt+200*i=10*e^(-R/L*t) Volts tau=1 time constant=L/R=0.002/200=0.00001 s--->100-((1-1/e^1)*100)=37%

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