00:01
So here in this question we are considering a half wave rectifier having voltage is given that is equal to 240 volt rms and the frequency is given that is equals to 60 hertz ac source.
00:12
We are given that the load is a series inductance resistance with the inductance l is given that is equal to 75 milli henry resistance is given that is equal to 10 ohm and the v of ac is given that is equals to 100 volt.
00:27
So in the first part we have to determine the power absorbed by the dc voltage.
00:32
So from here we are having the value of the v rms we are having the value of r l.
00:37
So v rms is equals to v of dc that is divided by the under root 2 from here.
00:41
So v of dc become equals to v of rms that is multiplied by under root 2.
00:46
So this from here is equals to 240 multiplied by the under root 2 that become equals to 339 .4 volt and the inductance is given as r raised to the power 2 plus omega of n to its whole square.
00:59
So plugging into the value here that is 10 raised to the power 2 plus 2 pi multiplied by 60 multiplied by 0 .075 to its whole square.
01:09
So simplifying the term we get the value of z that is equals to 30 ohm.
01:14
Now we can say that theta from here is equals to tangent inverse of omega l that is divided by r.
01:20
So plugging into the value that from here is equals to tangent inverse of omega that is 2 pi multiplied by 60 multiplied by 0 .075 that is divided by 10.
01:31
So simplifying the term we get the value of theta that is equals to 70 .52 degree or in radian it is 1 .23 radians.
01:39
So this is the value of the theta from here.
01:41
Now we are considering that is v of dc from here is equals to v of infinity which is multiplied by the sin of alpha from here.
01:48
So alpha from here is equals to sin inverse of v of dc that is divided by v of ac that from here is equals to sin inverse of 100 which is divided by 339 .41.
02:02
So simplifying the term from here we get the value of alpha that is equals to 0 .299 radian.
02:07
So this is the value of the alpha from here.
02:09
Now we are considering that is omega of t is equals to omega multiplied by l that is divided by r.
02:14
So this from here is equals to 377 which is multiplied by the 0 .075 that is divided by 10.
02:23
So the value of omega of tau from here will be equals to 2 .8275 and the value of i of omega of tau from here will be equals to v of dc divided by z multiplied by the sin of omega of t minus of theta minus of v of dc divided by r plus a e raised to the power minus a of t which is divided by omega of t.
02:43
So plug in all these values from here we get the value of a that become equals to 21 .2...