00:01
The current through the inductor is given by it is varying with respect to time and varying as i of t is equal to 3 minus 4 .5 e to the power minus 60 and correspondingly the inductance present in a circuit is 2 .5 henry.
00:25
Now we know that the potential difference across the inductor.
00:29
So if we have an inductor in the circuit, the potential difference v across an inductor is nothing but l, d, i, by dt, that is the magnitude.
00:38
So let us find out di by dt first and then find out the potential difference.
00:43
So di by dt is going to be d by dt of the current, which is 3 minus 4 .5, e to the power, minus 60.
00:52
So we have just considered v is equal to minus l, d, i by dt because according to lens law, we get the rate of change of flux is directly proportional to induced emf.
01:04
So v is going to be minus ldi by dt.
01:06
So differentiating this, d .i by dt is equal to 0 minus 4 .5 is a constant.
01:14
We'll take it outside.
01:15
E to the power minus 60 multiplied with minus 60.
01:20
So we are going to get d .i by dt as 4 .5 times 60 times e to the power minus 60.
01:29
2070 e to the power minus 60.
01:32
Now let us substitute and find out the magnitude of the voltage.
01:36
So magnitude of the voltage is going to be the inductance which is 2 .5 times.
01:43
2070 times a to the power minus 60.
01:47
So the potential difference across the inductor let us call it as vl...