A). Convert the following instantaneous currents to phasors,...

a). Convert the following instantaneous currents to phasors, using cos(?t) as the reference. Give your answers in both rectangular and polar form. (i) i(t) = 400?2 cos(?t - 30°) (ii) i(t) = 4 cos(?t - 30°) + 5?2 sin(?t + 15°). b) The instantaneous voltage across a circuit element is v(t) = 400 cos(?t + 25°) V, determine (i) the maximum value, (ii) the rms value, (iii) the phasor expression, using cos(?t) as the reference.

Transcript

00:01 So here in this question we have to convert the instantaneous current to the phasors.

00:04 So here we are considering about the first part here that is i of t become equals to 400 multiplied by the under root 2 multiplied by the cos of omega t minus 30 degree.

00:18 So this is given here we are considering about the i t.

00:21 So from here this is in the form of i t that is equals to i m which is multiplied by the cos of omega t minus 30 and the value of i rms from here become equals to i m which is divided by under root 2 that from here is equals to 400 multiplied by the under root 2 that is divided by under root 2 that from here is equals to 400.

00:42 So i from here is equals to i rms to the angle of theta that from here is equals to 400 to the angle of minus 30 degree.

00:51 This is for the polar form.

00:54 So the value of i from here is equals to 346 .41 minus j of 200.

01:00 This is for the rectangular form.

01:06 So this is the answer to the first part of the question.

01:09 Now we are considering about the second part where we are considering that is i t is equals to 4 cos of omega t minus 30 plus 5 under root 2 which is multiplied by the sin of omega t plus 15.

01:23 So this from here is equals to 4 cos of omega t minus 30 plus 5 multiplied by the under root 2 of cos of omega t plus 15 minus 90.

01:35 So simplifying the term we get the value of i of t from here that become equals to i m1 multiplied by the cos of omega t minus theta 1 plus i m2 which is multiplied by the cos of omega t minus of theta 2...

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