Solve b When voltages V1 70 sin 150pit and V2 240 cos 150p

Solve (b)

When voltages V_1 = 70 sin (150pit) and V_2 = 240 cos (150pit) are applied to the same circuit, the resulting voltage V is equal to their sum. (a) Graph V = V_1 + V_2 in the viewing rectangle [0,0.05,0.01] by [ - 280,280,40]. (b) Use the graph to estimate values for a and k so that V = a sin (150pit + k). Estimate the value of k between 0 and 2pi. (a) Which of the following correctly graphs V? (b) The value of a so that V = a sin (150pit + k) is. (Round to the nearest integer as needed.)

Solution

v1=70sin(150pi t) ,v2=240cos(150pi t)

v=v1+v2

v =70sin(150pi t) + 240cos(150pi t)

multiply and divide by [70² +240²]

v =[70² +240²] [(70/[70² +240²])sin(150pi t) + (240/[70² +240²])cos(150pi t)]

v =[70² +240²] [ sin(150pi t +k)]

a=[70² +240²]

a=250