QuestionAugust 18, 2025

Find the instantaneous voltage of a 1000 Hz sine wave when e=250vsin(omega t-60^circ ) at the instant t=0 a. -216.51v b. -205v C. -250v d. 250 V

Find the instantaneous voltage of a 1000 Hz sine wave when e=250vsin(omega t-60^circ ) at the instant t=0 a. -216.51v b. -205v C. -250v d. 250 V
Find the instantaneous voltage of a 1000 Hz sine wave when e=250vsin(omega t-60^circ ) at the instant t=0 a. -216.51v b. -205v C. -250v d. 250 V

Solution
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Answer

-216.51 V Explanation 1. Identify the formula for instantaneous voltage The formula is given as e = 250 \sin(\omega t - 60^\circ). 2. Calculate angular frequency \omega For a frequency of 1000 Hz, \omega = 2\pi f = 2000\pi rad/s. 3. Substitute t=0 into the equation Substitute t=0: e = 250 \sin(2000\pi \cdot 0 - 60^\circ) = 250 \sin(-60^\circ). 4. Calculate \sin(-60^\circ) \sin(-60^\circ) = -\sin(60^\circ) = -\frac{\sqrt{3}}{2}. 5. Compute the instantaneous voltage e = 250 \times -\frac{\sqrt{3}}{2} = -216.51 V.

Explanation

1. Identify the formula for instantaneous voltage<br /> The formula is given as $e = 250 \sin(\omega t - 60^\circ)$.<br />2. Calculate angular frequency $\omega$<br /> For a frequency of 1000 Hz, $\omega = 2\pi f = 2000\pi$ rad/s.<br />3. Substitute $t=0$ into the equation<br /> Substitute $t=0$: $e = 250 \sin(2000\pi \cdot 0 - 60^\circ) = 250 \sin(-60^\circ)$.<br />4. Calculate $\sin(-60^\circ)$<br /> $\sin(-60^\circ) = -\sin(60^\circ) = -\frac{\sqrt{3}}{2}$.<br />5. Compute the instantaneous voltage<br /> $e = 250 \times -\frac{\sqrt{3}}{2} = -216.51$ V.
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