suppose that at any tiem t(sec) the current i(amp) in an alternating current circuit is i=2cost+2sint. What is the peak (largest magnitude) current for this circuit?

Answer 1

d(i)/dt = -2sint + 2cost
= 0 for a max of i
solving this we get sint = cost
divide by cost
sint/cost = 1
tant = 1
t = pi/4 sec

then i = 2cos(pi/4) + 2sin(pi/4)
= √2 + √2
= 2√2 amps