Math Problem Statement
Solution
The image shows a circuit with an AC input of 120 Vrms passing through several components: a transformer, full-wave rectifier, filter, 5V regulator, and a load. The question is asking for the voltage at point C, which is after the full-wave rectifier.
Here's a breakdown:
- Input voltage at A (AC input) is 120 Vrms.
- The transformer has a 10:1 ratio, meaning it steps down the voltage. The secondary side at B would have:
- After the full-wave rectifier at point C, the peak voltage can be calculated from the RMS voltage:
- However, the full-wave rectifier introduces a diode drop (about 2 diode voltage drops in total for a full-wave rectifier using silicon diodes), which subtracts around 1.4V (0.7V per diode). This results in:
Therefore, the voltage at point C is approximately 15.6 Vp.
The correct option is 15.6 Vp.
Do you want more details or have any questions?
Here are 5 related questions for further exploration:
- What is the difference between peak and RMS voltage?
- How does a transformer step down voltage?
- Why do rectifiers drop voltage, and how is the drop calculated?
- What role does a filter play in this circuit?
- What is the purpose of the 5V regulator in this circuit?
Tip: In full-wave rectification, both halves of the AC signal are used, which improves efficiency compared to half-wave rectification.
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Math Problem Analysis
Mathematical Concepts
Electrical Engineering
AC to DC Conversion
Transformer Voltage Step-Down
Rectification
Formulas
V_rms = V_peak / sqrt(2)
Transformer Voltage Step-Down: V_secondary = V_primary / N_turns
Peak Voltage after Rectification: V_peak = V_rms * sqrt(2)
Diode Drop in Full-Wave Rectifier: V_diode ≈ 0.7V (per diode)
Theorems
AC to DC Conversion using a Full-Wave Rectifier
Transformer Ratio Theorem
Suitable Grade Level
Undergraduate Electrical Engineering
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