00:01
In this equation, at the time t which is less than 0, we can write current i, o, which is equal to 0, ampure, since the source is not connected to the inductor, then at the time t, which is equals to alpha, e, then we have the value of a inductance l, which is equal to 10 -handry.
00:31
Current law it can be written as a 15 v a minus 15 divided by 20 plus va divided by 20 plus va divided by 20 which is equals to 0 therefore we can write va multiplied by 1 plus 1 plus 1 plus 1 divided by 20 which is equals to 15 divided by 20 so on a in simplification, we get the value of va which is equals to 5 watt.
01:07
So this is the first value and using that we can find out the current at alpha e which is equal to va divided by 20.
01:16
So it becomes 5 divided by 20 which is equals to 0 .25 ampere.
01:23
Now we can find out the equivalent resistor but for that we need to draw circuit.
01:31
So it can be drawn as here we have this 20 oom and 20 om which are connected in series with a parallel connection that is again a 20 oom so we need to find out here this are equivalent so it can be written as r equivalent which is equals to 20 multiplied by 20 divided by 20 plus 20 n is connected in series, so it's a 20, so total becomes a 30 om.
02:15
Then time constant, thou, which is equal to l divided by r equivalent, so it can be written as 10 divided by 30, so it becomes a 1 divided by 3 second.
02:28
Now we can write down the equation of current it, which is equals to i -alphae, multiplied by 1 minus e to the power minus t divided by thou...