Question

Two sinusoidal currents are given as: i1 = 10√2 sin wt and i2 = 20√2 sin (wt +

60o

). Find the expression for the sum of theses currents.​

Answer 1

Answer:

answer is given in the attachment....

Answer 2

Answer:

CONCEPT:

• Sinusoidal waveforms are periodic waveforms which can be plotted or drawn in sine or cosine functions in the trigonometry.
• Sinusoidal waveforms are added in vectors form
• Sinusoidal waveforms can also be added by finding their components in x and y-axis , then adding them and then finding the resultant of it.

GIVEN:

• $i1=10\sqrt{2}$sin wt
• $i2=20\sqrt{2}$sin(wt+60°)

TO FIND:

Expression for sum of currents

SOLUTION:

To add the currents, first we will find their component in x and y-axis the then add in their respective axis.

In x-axis,

current i1 has it's component in only x-axis as angle is 0°=$10\sqrt{2}$

current i2 has it's component in x-axis= $20\sqrt{2}$cos 60

Total current in x-axis =$10\sqrt{2}+20\sqrt{2}$cos60

⇒$10\sqrt{2} +20\sqrt{2}.\frac{1}{2}$

⇒$10\sqrt{2} +10\sqrt{2}$

⇒$20\sqrt{2}$

In y-axis,

There is no component of i1 current.

current 12 has it's component in y-axis = $20\sqrt{2}$sin 60

⇒$20\sqrt{2}.\frac{\sqrt{3} }{2}$

⇒$10\sqrt{6}$

Now the resultant of both the components will give the current

⇒$\sqrt{(20\sqrt{2}) ^{2}+(10\sqrt{6} )^{2} }$

⇒$\sqrt{400.2+100.6}$

⇒$\sqrt{800+600}$

⇒$\sqrt{1400}$

⇒$10\sqrt{14}$

So, the resultant current is,

$i=10\sqrt{14}$sin(wt+40.9)

To solve similar questions,

https://brainly.in/question/21333177

https://brainly.in/textbook-solutions/q-70-alternating-currents-given-i1-i0-sin

Thank you