What are the peak-to-peak and maximum values of alternating current if the RMS value is 12 A?

What are the peak-to-peak and maximum values of alternating current if the RMS value is 12 A?

• A. 16.97 A, 33.94 A
• B. 14 A, 28 A
• C. 15 A, 30 A
• D. 20 A, 40 A

Answer: (A)

To determine the peak-to-peak and maximum values of alternating current when given the RMS (root mean square) value, it's essential to understand the relationship between these values. The RMS value is a measure of the effective value of an alternating current, and for a sinusoidal waveform, it can be related to the peak value (also known as the maximum value) using the formula: \[ I_{rms} = \frac{I_{peak}}{\sqrt{2}} \] From this equation, we can derive the peak value: \[ I_{peak} = I_{rms} \cdot \sqrt{2} \] Substituting the given RMS value of 12 A: \[ I_{peak} = 12 \, A \cdot \sqrt{2} \approx 12 \, A \cdot 1.414 = 16.97 \, A \] The peak-to-peak value is essentially double the peak value because it measures the total swing of the waveform from its maximum positive value to its maximum negative value: \[ I_{peak-to-peak} = 2 \cdot I_{peak} = 2 \cdot 16.

To determine the peak-to-peak and maximum values of alternating current when given the RMS (root mean square) value, it's essential to understand the relationship between these values. The RMS value is a measure of the effective value of an alternating current, and for a sinusoidal waveform, it can be related to the peak value (also known as the maximum value) using the formula:

[

I_{rms} = \frac{I_{peak}}{\sqrt{2}}

]

From this equation, we can derive the peak value:

[

I_{peak} = I_{rms} \cdot \sqrt{2}

]

Substituting the given RMS value of 12 A:

[

I_{peak} = 12 , A \cdot \sqrt{2} \approx 12 , A \cdot 1.414 = 16.97 , A

]

The peak-to-peak value is essentially double the peak value because it measures the total swing of the waveform from its maximum positive value to its maximum negative value:

[

I_{peak-to-peak} = 2 \cdot I_{peak} = 2 \cdot 16.