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In an AC circuit, if the voltage is given as V(t) = 100√2 sin(ωt), what is the R

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Question: In an AC circuit, if the voltage is given as V(t) = 100√2 sin(ωt), what is the RMS voltage?

Options:

  1. 100 V
  2. 70.71 V
  3. 141.42 V
  4. 50 V

Correct Answer: 70.71 V

Solution: 

The RMS voltage (V_rms) for a sinusoidal waveform is V_peak / √2, so V_rms = 100√2 / √2 = 100 V.

In an AC circuit, if the voltage is given as V(t) = 100√2 sin(ωt), what is the R

Practice Questions

Q1
In an AC circuit, if the voltage is given as V(t) = 100√2 sin(ωt), what is the RMS voltage?
  1. 100 V
  2. 70.71 V
  3. 141.42 V
  4. 50 V

Questions & Step-by-Step Solutions

In an AC circuit, if the voltage is given as V(t) = 100√2 sin(ωt), what is the RMS voltage?
  • Step 1: Identify the given voltage function, which is V(t) = 100√2 sin(ωt).
  • Step 2: Recognize that the term '100√2' represents the peak voltage (V_peak) of the waveform.
  • Step 3: Recall the formula for calculating RMS voltage (V_rms) for a sinusoidal waveform, which is V_rms = V_peak / √2.
  • Step 4: Substitute the peak voltage into the formula: V_rms = (100√2) / √2.
  • Step 5: Simplify the expression: V_rms = 100 V.
  • RMS Voltage Calculation – Understanding how to calculate the root mean square (RMS) voltage from a sinusoidal voltage function.
  • Sinusoidal Waveforms – Recognizing the characteristics of sinusoidal waveforms and their peak and RMS values.
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