If current I1= 3A sin wt and I2= 4A cos wt, then I3 is: Experts in the solution - Physics - Alternating Current

Question

If current I1= 3A sin wt and I2= 4A cos wt, then I3 is: Experts in
the solution given below why we are multiplying and dividing
particularly with 5

Rohit Babu · Accepted Answer

Dear Student,Given,I1=3Asinωt, I2=4AcosωtWe need to find I3 using junction rule
⇒I3=I1+I2=3Asinωt+4AcosωtDividing and multiplying by 5I3=5×35Asinωt+5×45Acosωt=5A×(35sinωt+45cosωt)[By doing this we can substitute cos530=35 and sin530=45 in the next step and finally apply the formula of sin(A+B)]⇒I3=5A×cos530 sinωt+ sin530 cosωtI3=5A(sinωt cos530+cosωt sin530)
(1)Here, A=ωt and B=530We have,sinA cosB+cosA sinB=sin(A+B)Thus, equation 1 becomes,I3=5Asin(ωt+530)Regards

If current I1= 3A sin wt and I2= 4A cos wt, then I3 is: ..Experts in the solution given below why we are multiplying and dividing particularly with 5