SOLUTION: please help me answer this question:
"Two voltages:
V1 = 3 cos(5t), V2 = 4 sin(5t)
are inputs to a circuit. Determine an expression for the output voltage, v, if this is given
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-> SOLUTION: please help me answer this question:
"Two voltages:
V1 = 3 cos(5t), V2 = 4 sin(5t)
are inputs to a circuit. Determine an expression for the output voltage, v, if this is given
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Question 1115565: please help me answer this question:
"Two voltages:
V1 = 3 cos(5t), V2 = 4 sin(5t)
are inputs to a circuit. Determine an expression for the output voltage, v, if this is given by:
V = V1 + V2 = A sin(5t + α)
i.e. determine the values of A and α, where α is in radians" Answer by ikleyn(52817) (Show Source):
V1 + V2 = 3*cos(5t) + 4*sin(5t) = (1)
Since = = 1, there is (= does exist) the angle "a" in QI such that sin(a) = , cos(a) = .
With these identities, we can continue (1) in this way:
V1 + V2 = 3*cos(5t) + 4*sin(5t) = = 5*(cos(5t)*sin(a) + sin(5t)*cos(a)) (2)
Now apply the sine addition formula, and you can continue (2) in this way
V1 + V2 = = = 5*(cos(5t)*sin(a) + sin(5t)*cos(a)) = 5*sin(5t+a).
It is just what the problem wants of you with A = 5 and = a = = .
