Sinusoidal%20Alternating%20Voltage

Sinusoidal%20Alternating%20Voltage - ACC AC CIRCUITS...

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ACC AC CIRCUITS v = V m sin ϖ t = V m sin (2 π f) t ϖ = radian frequency (in rad / s) f = frequency (in cycle/s or Hz [Hertz]) If f = 60 Hz, ϖ would be equal to (2 π )(60) = 377 rad / s Resistor Sinusoidal Response i = V / R For v = V m sin ϖ t: i = V R t m sin ϖ and Power = V i = V R t m 2 2 sin ϖ 1 Time
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ACC The above power is instantaneous power – that is at any time, the power is different. If we want to find the power consumed over one complete cycle, then: Average Power = ϖ π ϖ π ϖ 2 V R m 0 2 2 sin 2 t dt = ( 29 V R 2 1- cos 2 t m 0 2 2 ϖ π ϖ π ϖ 2 dt = V R t t m 2 2 1 2 1 4 2 0 2 π ϖ ϖ π ϖ - sin = V R V R V m m m 2 2 2 2 2 ϖ π π ϖ = = I m RMS Voltage If a DC voltage source with a voltage of V 0 is connected to a resistor of resistance R, the power in the circuit would be constant and equal to: P = V 0 I = V 0 2 / R If the voltage source is a sinusoidal function, V(t) where:
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Sinusoidal%20Alternating%20Voltage - ACC AC CIRCUITS...

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