Math Problem Statement

What is the voltage at point C? Assume the AC input is 120 Vrms.

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:

  1. Input voltage at A (AC input) is 120 Vrms.
  2. The transformer has a 10:1 ratio, meaning it steps down the voltage. The secondary side at B would have: VB=120 Vrms10=12 VrmsV_{B} = \frac{120 \text{ Vrms}}{10} = 12 \text{ Vrms}
  3. After the full-wave rectifier at point C, the peak voltage VpV_p can be calculated from the RMS voltage: Vp=Vrms×2=12×1.41416.97 VV_p = V_{rms} \times \sqrt{2} = 12 \times 1.414 \approx 16.97 \text{ V}
  4. 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: Vp16.971.4=15.57 VV_p \approx 16.97 - 1.4 = 15.57 \text{ V}

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:

  1. What is the difference between peak and RMS voltage?
  2. How does a transformer step down voltage?
  3. Why do rectifiers drop voltage, and how is the drop calculated?
  4. What role does a filter play in this circuit?
  5. 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