Asked Jan 16, 2020

Suppose that at any given time t (in seconds) the current i (in amperes) in an alternating current circuit is i = 2 cos t + 2 sin t. What is the peak current for this circuit (largest magnitude)


Expert Answer

Step 1

Factor out 2 from expression of i.

Calculus homework question answer, step 1, image 1
Step 2

We'll try to express (cost+sint) as an expression of sine. For that we multiply by 1/sqrt(2) with (cost+sint)

And by sqrt(2) outside to balance.

Calculus homework question answer, step 2, image 1
Step 3

We know that cos(pi/4)=sin(pi/4) = 1/sqrt(2) ...

Calculus homework question answer, step 3, image 1

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