00:01
All right, so consider the shown circuit with the capacitor initially uncharged.
00:07
When the switch s is moved to point a and the capacitor starts changing, starts charging, you can say.
00:17
Find the time it takes the capacitor to be charged by 25 % of its final charge.
00:26
Right.
00:27
So now basically, if switch is moved to be charged.
00:31
Point a this is the concept this is the point the problem says so now what will be the diagram first of all we will see that so this will be the diagram so this is short -circuited with point a and we have here one battery of 60 volts isn't it so same is there right one one mega -oom and we have three mega -o and two mega -o right so we need to to write here like this this is 3 mega -oom and we have here 2 mega -oom and here we have 1 mega which is open circuited isn't it 1 mega -o so you can say that no current flows across 1 mega -o right so here the one capacitor is there which has the value 10 micro -farrid so this is the diagram here, right? but we will also write r equivalent because in the formula we have to use r equivalent, right? so this can be redrawn as this circuit diagram is redrawn as like this.
01:56
We have here capacitor and we have here battery.
02:01
Now here we have, i'm sorry.
02:04
Now here we have one.
02:11
Okay.
02:12
So, so this is 5 mega -oom, why? because there is 3 mega -oom and 2 -mm are in series.
02:23
While across 1 megam there is no current flow, right? no current i equals to 0, you can say.
02:33
Right.
02:34
So this will be again 60 volts only, right? this will be 10 micro -parad.
02:40
Okay.
02:42
So now what will be the following? so formula for charge of capacitor varying as a function of time which could be expressed as qt equals to c e multiplied by 1 minus e to 3 power minus t by r equivalent.
03:03
Equivalent resistance we have to take multiplied by c that is rc you can say right here we will take our equivalent equivalent okay okay.
03:14
So now it has already told that capacitor takes, it is 25 % charge, right? so that means 0 .25 times of ce.
03:33
So from equation 1 and 2, can you conclude something? yes.
03:38
So now you may write one equation here.
03:40
So this is ce and ce is going to be cancelled, right? so let me just try it here.
03:46
So this is 0 .25 c .e.
03:50
Equals to ce from equation 1 let me write first and 2 .25 ce equals to ce 1 minus e to the power minus t by 5 into 10 isn't it so now this becomes equals to let me just cancel it out so this c e c c c c c c cancels each other right and you just just need to segregate these values.
04:36
So here it becomes e to the power minus t by 50.
04:40
Right? so this comes minus e this comes this side and we just need to subtract from 1 minus 0 .25...