00:01
So, let us start with the concept which we are going to use here for this question.
00:07
Since we know that the current or the capacitor can be given by i is equals to 6 times of dv by dt.
00:16
So according to question we are given a capacitor something like in this way which is connected across a current source of i of t which is something like in this way whose direction is upward and this is connected across plus minus of this capacitor with voltage of vc of t.
00:42
So, you have to find the relation between the current and voltage for the a part.
00:49
So, as you can see the input is x of t which is equals to the current function that is i of t and output is what y of t which is equals to vc of t.
01:01
So, according to the concept for a part since we know that current is equals to this c dv by dt.
01:11
So, plugging the values the current i of t will be goes to c dvc of t divided by dt or you can write vc of t this should be equals to 1 over c integration i of t dt.
01:29
If we take all the terms aside so obviously derivative will becomes in the form of integral.
01:35
So, this is what the required answer for a part of this question.
01:42
Now let's have a look to b part.
01:44
First of all as we have seen above the current i of t is equals to c dvc of t by dt or in integral form we have seen that...