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An ac voltage is described by v(t) = 10 cos (400 πt), find out frequency and RMS value of voltage.
- a)400 Hz, 7.07V
- b)400 Hz, 14.14V
- c)200 Hz, 14.14V
- d)200 Hz, 7.07V
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
An ac voltage is described by v(t) = 10 cos (400 πt), find out freq...
V(t) = 10 cos (400 π t)
ω = 400 π
⇒ 2 π f = 400 π
⇒ f = 200 Hz
Vm = 10 V
Most Upvoted Answer
An ac voltage is described by v(t) = 10 cos (400 πt), find out freq...
Understanding the AC Voltage Function
The given voltage function is:
v(t) = 10 cos(400πt)
This expression describes an alternating current (AC) voltage, where:
- **Amplitude (A)** = 10 V (the peak voltage)
- **Angular frequency (ω)** = 400π rad/s
Finding the Frequency
The frequency (f) can be derived from the angular frequency using the formula:
f = ω / (2π)
Substituting the given angular frequency:
- ω = 400π rad/s
- f = (400π) / (2π) = 200 Hz
This indicates that the frequency of the voltage is **200 Hz**.
Calculating the RMS Value
The root mean square (RMS) value of an AC voltage is calculated using the formula:
RMS = A / √2
Where A is the amplitude. Therefore:
- A = 10 V
- RMS = 10 / √2 ≈ 10 / 1.414 ≈ 7.07 V
Thus, the RMS value of the voltage is approximately **7.07 V**.
Final Answer
Combining both results, we find that:
- Frequency = 200 Hz
- RMS Voltage = 7.07 V
The correct answer is option **D) 200 Hz, 7.07 V**.
The given voltage function is:
v(t) = 10 cos(400πt)
This expression describes an alternating current (AC) voltage, where:
- **Amplitude (A)** = 10 V (the peak voltage)
- **Angular frequency (ω)** = 400π rad/s
Finding the Frequency
The frequency (f) can be derived from the angular frequency using the formula:
f = ω / (2π)
Substituting the given angular frequency:
- ω = 400π rad/s
- f = (400π) / (2π) = 200 Hz
This indicates that the frequency of the voltage is **200 Hz**.
Calculating the RMS Value
The root mean square (RMS) value of an AC voltage is calculated using the formula:
RMS = A / √2
Where A is the amplitude. Therefore:
- A = 10 V
- RMS = 10 / √2 ≈ 10 / 1.414 ≈ 7.07 V
Thus, the RMS value of the voltage is approximately **7.07 V**.
Final Answer
Combining both results, we find that:
- Frequency = 200 Hz
- RMS Voltage = 7.07 V
The correct answer is option **D) 200 Hz, 7.07 V**.
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Question Description
An ac voltage is described by v(t) = 10 cos (400 πt), find out frequency and RMS value of voltage.a)400 Hz, 7.07Vb)400 Hz, 14.14Vc)200 Hz, 14.14Vd)200 Hz, 7.07VCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about An ac voltage is described by v(t) = 10 cos (400 πt), find out frequency and RMS value of voltage.a)400 Hz, 7.07Vb)400 Hz, 14.14Vc)200 Hz, 14.14Vd)200 Hz, 7.07VCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ac voltage is described by v(t) = 10 cos (400 πt), find out frequency and RMS value of voltage.a)400 Hz, 7.07Vb)400 Hz, 14.14Vc)200 Hz, 14.14Vd)200 Hz, 7.07VCorrect answer is option 'D'. Can you explain this answer?.
An ac voltage is described by v(t) = 10 cos (400 πt), find out frequency and RMS value of voltage.a)400 Hz, 7.07Vb)400 Hz, 14.14Vc)200 Hz, 14.14Vd)200 Hz, 7.07VCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about An ac voltage is described by v(t) = 10 cos (400 πt), find out frequency and RMS value of voltage.a)400 Hz, 7.07Vb)400 Hz, 14.14Vc)200 Hz, 14.14Vd)200 Hz, 7.07VCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ac voltage is described by v(t) = 10 cos (400 πt), find out frequency and RMS value of voltage.a)400 Hz, 7.07Vb)400 Hz, 14.14Vc)200 Hz, 14.14Vd)200 Hz, 7.07VCorrect answer is option 'D'. Can you explain this answer?.
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