The two switches shown in the circuit in Fig. P 7.19 operate...

The two switches shown in the circuit in Fig. $P 7.19$ operate simultaneously. Prior to $t=0$ each switch has been in its indicated position for a long time. At $t=0$ the two switches move instantaneously to their new positions. Find a) $v_{d}(t), t \geq 0^{+}$ b) $i_{0}(t), t \geq 0$

Transcript

00:01 So, let us start with the concept which we are going to use here for this question.

00:05 So, according to definition equation of voltage of inductor v is equals to l into di of t by dt where l is the inductor.

00:15 Now v is the voltage, l is the inductance in henry and i is the current in ampere, t is the time in second.

00:21 So, from the first we can able to determine the current di would be equals to the 1 over l times of v times of dt.

00:29 So, from here current i would be equals to the 1 over l integration of from initial time t naught to the final time t into v dt plus the initial case current that i t of naught.

00:46 Let us say this as equation number, ok let us say this as 1 and this as second.

00:52 Now, from equation for series connection of inductor, what we can do that, that is for series connection of inductors, the l equivalent will be calculated by the means of formula l1 plus l2.

01:08 Similarly, for parallel combinations of two resistors, the equivalent can be calculated 1 by equivalent equals to 1 by l1 plus 1 by l2.

01:20 So, from here this l equivalent will be goes to l1 into l2 by l1 plus of l2.

01:29 So, basically for the a part, since the switches have been closed for a long time.

01:34 So, for the a part, since that the switches have been closed for a long time that means t tending to infinity, that means the inductance l should be equals to the 20 milli henry this we have been given and it's tending up to the 80 of milli henry inductors access the short circuited means this both inductor is going to be short circuited while the 48 milli henry of inductor and 2 .5 kilo hertz of resistor will be open circuited.

02:09 Ok, this both will be short circuited and this both will be open circuited.

02:16 So, on the picture one we can see that that is so let me draw the figure first.

02:21 As you can see into the circuit that i have been shown this by short circuited and open circuited combination.

02:29 So, by using these equations we can calculate the l equivalent...

Question

The two switches shown in the circuit in Fig. $P 7.19$ operate simultaneously. Prior to $t=0$ each switch has been in its indicated position for a long time. At $t=0$ the two switches move instantaneously to their new positions. Find a) $v_{d}(t), t \geq 0^{+}$ b) $i_{0}(t), t \geq 0$

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