Find the average value of the full-wave rectified output voltage if the input voltage is 45 V.
A. 3.86478 V
B. 28.6478 V
C. 38.6478 V
D. 2.8478 V
E. None of the above.
Answer (2)
The average value of the full-wave rectified output voltage for a peak input voltage of 45 V is approximately 28.6478 V. This is calculated using the formula V a vg = π 2 V p . The correct answer from the choices given is option B: 28.6478 V.
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Use the formula for the average voltage of a full-wave rectifier: V a vg = π 2 V p .
Substitute the given peak voltage V p = 45 V into the formula: V a vg = π 2 ( 45 ) .
Calculate the average voltage: V a vg = π 90 ≈ 28.6478 V.
The average value of the full-wave rectified output voltage is 28.6478 V .
Explanation
Problem Analysis and Formula We are asked to find the average value of a full-wave rectified output voltage given the peak input voltage. The formula for the average voltage ( V a vg ) of a full-wave rectified voltage in terms of the peak voltage ( V p ) is: V a vg = π 2 V p where V p is the peak voltage.
Substitution We are given that the input voltage V p = 45 V. We substitute this value into the formula: V a vg = π 2 × 45
Calculation Now, we calculate the average voltage: V a vg = π 90 ≈ 28.6478 V
Comparison and Answer Comparing the calculated value with the given options, we find that option (b) matches our result.
Examples
Full-wave rectifiers are commonly used in power supplies to convert AC voltage to DC voltage. Knowing the average output voltage is crucial for designing and analyzing such circuits. For example, if you are designing a power supply for a device that requires 28.6 V DC, you would need to ensure that the full-wave rectifier circuit provides this average voltage given a specific AC input. This involves selecting appropriate components and designing the circuit to achieve the desired output. Understanding the relationship between peak voltage and average voltage is essential for efficient power supply design.
