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A sinusoidally varying potential difference has an amplitude of 170 V. What is its rms value?

a) 170 V
b) 120 V
c) 0
d) -120 V
e) -170 V

Answer :

In physics, the root mean square (RMS) value of a sinusoidal waveform is a measure of the effective or average value of the waveform. For a sinusoidally varying voltage, the RMS value is a way to express the power-bearing capability of the waveform compared to a DC voltage.

To calculate the RMS value of a sinusoidal AC voltage given its amplitude, we use the formula:

[tex]V_{rms} = \frac{V_{peak}}{\sqrt{2}}[/tex]

Where:

  • [tex]V_{rms}[/tex] is the root mean square value.
  • [tex]V_{peak}[/tex] is the peak or amplitude value of the voltage.

Given in the question, the amplitude ([tex]V_{peak}[/tex]) is 170 V.

Let's calculate the RMS value:

[tex]V_{rms} = \frac{170\, \text{V}}{\sqrt{2}} \approx \frac{170\, \text{V}}{1.414} \approx 120.2\, \text{V}[/tex]

Therefore, the RMS value is approximately [tex]120 \, \text{V}[/tex], which corresponds to option b) in the multiple choice answers.

Thus, the correct choice is b) 120 V.

The RMS value is important in circuits when determining how much power is used or needed since it represents the equivalent DC value in terms of power dissipation.

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