What is the maximum value of the AC voltage whose root-mean-square value is (a) \(110 \mathrm{~V}\) or (b) \(220 \mathrm{~V} ?\)

Short Answer

Expert verified
Answer: (a) The maximum value of the AC voltage with an RMS value of 110 V is approximately 155.56 V. (b) The maximum value of the AC voltage with an RMS value of 220 V is approximately 311.13 V.

Step by step solution

01

Write down the given RMS values

We are given the RMS values of two AC voltages as: (a) \(V_\mathrm{rms} = 110 \mathrm{~V}\) (b) \(V_\mathrm{rms} = 220 \mathrm{~V}\)
02

Calculate the maximum value of the AC voltage for part (a)

Using the relationship between the maximum value and the RMS value of an AC voltage, we can find the maximum value for part (a): \(V_\mathrm{max} = \sqrt{2} \times V_\mathrm{rms}\) For part (a), \(V_\mathrm{rms} = 110 \mathrm{~V}\), so we have: \(V_\mathrm{max} = \sqrt{2} \times 110 \mathrm{~V} \approx 155.56 \mathrm{~V}\)
03

Calculate the maximum value of the AC voltage for part (b)

Similarly, we can find the maximum value for part (b). For part (b), \(V_\mathrm{rms} = 220 \mathrm{~V}\), so we have: \(V_\mathrm{max} = \sqrt{2} \times 220 \mathrm{~V} \approx 311.13 \mathrm{~V}\)
04

Write down the final answers

The student can now write the final answers for the maximum value of the AC voltage for both given RMS values: (a) The maximum value of the AC voltage with an RMS value of \(110 \mathrm{~V}\) is approximately \(155.56 \mathrm{~V}\). (b) The maximum value of the AC voltage with an RMS value of \(220 \mathrm{~V}\) is approximately \(311.13 \mathrm{~V}\).

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