Question

2) What is 1(), the magnitude of the current through the resistor R after the switch has been closed for a very long time? A Submit 3) What is l_(-), the magnitude of the current through the inductor after the switch has been closed for a very long time? A Submit 4) After the switch has been closed for a very long time, it is then opened. What is Iz(topen), the current through the resistor R3 at a time topen - 8.1 ms after the switch was opened? The positive direction for the current is indicated in the figure. A Submit 5) What is L.max(closed), the magnitude of the maximum voltage across the inductor during the time when the switch is closed? V Submit Copen), the magnitude of the maximum voltage across the inductor during the time when the switch is 61 What is open? V Submt r ola some once to write moto

Answer 1

a)

Immediately after switch is closed at t=0 ,inductor will act as open circuit .Therefore equivalent resistor is

R=27+68+85 =180 ohms

The Magnitude of current through the resistor R4 is

I₄(0)=V/R =12/180 =0.066666667 A

b)

After Long time switch is closed ,inductor will act as short circuit .therefore

R=27 + 85 +(1/27 +1/68)^-1 = 131.33 ohms

The Magnitude of current through the resistor R4 is

I₄(infinity)=V/R =12/131.33=0.09137544 A

c)

Current through the inductor is

I_L(infinity)=0.09137544*(68/68+27) =0.047719298 A

d)

With switch opened ,time constant is

T=L/(R₂+R₃) = 320/(27+68) =3.368421053 ms

For RL circuit discharging

I=-I_oe^-t/T

I = -0.047719298e^{-8.1/3.368421053}

I=-0.004308752359 A

e)

Maximum Voltage across the inductor when the swithc is closed is

V_L,max(closed)=0.06666667*68=4.5333333 V

f)

Maximum Voltage across the inductor when the switch is open is

V_L,max(open)=0.047719298*(27+68)=4.5333333 V