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If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS c

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Question: If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS current? (2021)

Options:

  1. 5 A
  2. 2.5 A
  3. 7.07 A
  4. 3.54 A

Correct Answer: 2.5 A

Solution: 

The RMS current is I_rms = I_peak / √2 = 5√2 / √2 = 5 A.

If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS c

Practice Questions

Q1
If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS current? (2021)
  1. 5 A
  2. 2.5 A
  3. 7.07 A
  4. 3.54 A

Questions & Step-by-Step Solutions

If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS current? (2021)
  • Step 1: Identify the given current function, which is I(t) = 5√2 sin(100t + π/4).
  • Step 2: Recognize that the term '5√2' in the function represents the peak current (I_peak).
  • Step 3: Recall the formula to find the RMS (Root Mean Square) current, which is I_rms = I_peak / √2.
  • Step 4: Substitute the peak current into the formula: I_rms = (5√2) / √2.
  • Step 5: Simplify the expression: I_rms = 5 A.
  • RMS Current Calculation – The RMS (Root Mean Square) current in an AC circuit is calculated by dividing the peak current by the square root of 2.
  • Understanding AC Current Waveforms – Recognizing the form of the AC current equation and identifying the peak current from it.
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