Math Problem Statement
Solution
The circuit in the image shows an AC voltage source that goes through several stages: a transformer, a full-wave rectifier, a filter, a 5V regulator, and a load. The key question is determining the voltage at point D, which is just after the filter.
Here's a breakdown of the circuit:
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AC Input: The input is 120 Vrms (root mean square). This is the voltage entering the transformer.
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Transformer: The transformer has a 10:1 step-down ratio, meaning the output at point B (secondary side of the transformer) will be 10 times lower than the input voltage.
- The input is 120 Vrms, so the output at point B will be: The transformer steps the voltage down to 12 Vrms.
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Full-Wave Rectifier: After the transformer, the full-wave rectifier converts the AC voltage into pulsating DC. The rectified voltage (peak voltage, ) can be calculated from the Vrms value. The relationship between Vrms and peak voltage is: So, the peak voltage after rectification is: Therefore, the peak rectified voltage is about 16.97 V.
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Filter: The filter smooths out the pulsating DC to provide a near-constant DC voltage. For ideal filtering, the output voltage at point D would be close to the peak value from the rectifier, minus any small losses in the components. So, at point D, the voltage is approximately 16.97 V DC.
Thus, the voltage at point D is approximately 16.97 V DC.
Let me know if you need more details or explanations.
Follow-up Questions:
- How does the full-wave rectifier work in converting AC to DC?
- What role does the filter play in smoothing the DC voltage?
- Why is the Vrms lower than the peak voltage?
- What kind of filter is typically used in such circuits (e.g., capacitor filter)?
- How would the output change if the transformer ratio was different?
Tip:
To accurately calculate DC voltage after rectification, always remember to account for the diode drops in a real-world circuit, typically around 0.7V per diode in silicon diodes.
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Math Problem Analysis
Mathematical Concepts
AC to DC Conversion
Transformers
Rectification
Voltage Calculation
Formulas
V_rms = V_peak / √2
V_peak = V_rms × √2
Transformer Step-Down Ratio: V_secondary = V_primary / Turns Ratio
Theorems
RMS to Peak Voltage Relationship
Suitable Grade Level
College (Electrical Engineering)
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