If v(t) is 50V at α = 45° and t = 1 ms, what is the mathematical expression for the sinusoidal voltage?Group of answer choicesv(t) = 50sin45°v(t) = 70.71sin785.4tv(t) = 70.71sin45°tv(t) = 50sin785.4t Previous
Question
If v(t) is 50V at α = 45° and t = 1 ms, what is the mathematical expression for the sinusoidal voltage?Group of answer choicesv(t) = 50sin45°v(t) = 70.71sin785.4tv(t) = 70.71sin45°tv(t) = 50sin785.4t Previous
Solution
The mathematical expression for the sinusoidal voltage is v(t) = 50sin785.4t. This is because in a sinusoidal function, the amplitude (maximum value) is 50V as given. The angle α is 45° but we need to convert this to radians for the function, and the time t is 1ms. The frequency of the sinusoidal function is 1/t, which is 1000Hz or 1000 cycles per second. Since there are 2π radians in one cycle, the angular frequency is 2π1000 = 2000π rad/s or 2000π10^3 mrad/ms which is approximately 785.4 mrad/ms. Therefore, the function is v(t) = 50sin(785.4t).
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