Because of Euler’s formula, it is often convenient to

QUESTION:

Because of Euler’s formula, it is often convenient to treat the voltage sources E0cos ?t and E0 sin?t simultaneously, using In this case, equation (3) becomes where q is now complex (recall I = q’,I’ = q’’).(a) Use the method of undetermined coefficients to show that the steady-state solution to (22) is The technique is discussed in detail in Project F at the end of Chapter 4.(b) Now show that the steady-state current is (c) Use the relation where tan ? = ?/?, to show that Ip can be expressed in the form where tan ? = (1/C – L?2)/(?R).(d) The imaginary part of ei?t is sin ?t, so the imaginary part of the solution to (22) must be the solution to equation (3) for E(t) = E0 sin?t. Verify that this is also the case for the current by showing that the imaginary part of Ip in part (c) is the same as that given in equation (10).