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A sinusoidal current i = I cosωt has an rms value I_rms = 2.10 A. (a) What is the current amplitude?
31. Alternating Current
Alternating Voltages and Currents
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An AC emf source is given by . What is the instantaneous emf of this source at?
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Verified step by step guidance1
Identify the given AC emf equation: \( \mathcal{E} = (170\, \text{V}) \cos(2\pi(60\, \text{Hz})t) \). This represents the instantaneous emf as a function of time.
Substitute the given time \( t = 97\, \text{ms} = 0.097\, \text{s} \) into the equation. This requires converting milliseconds to seconds for consistency in units.
Calculate the angular frequency \( \omega \) using the formula \( \omega = 2\pi f \), where \( f = 60\, \text{Hz} \). This gives \( \omega = 2\pi \times 60 \).
Substitute \( \omega \) and \( t \) into the cosine function: \( \cos(2\pi \times 60 \times 0.097) \).
Evaluate the cosine function to find the instantaneous emf at \( t = 0.097\, \text{s} \). Multiply the result by the amplitude (170 V) to get the instantaneous emf value.
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