Question

What is the dc component of the output voltage if a sinusoidal signal of \(33\,\text{V}\) peak voltage is the input of a half wave diode rectifier circuit?

• A. \(3.5\,\text{V}\)
• B. \(2.9\,\text{V}\)
• C. \(10.5\,\text{V}\)
• D. \(12.5\,\text{V}\)

Hint:

Half-wave rectifier output average voltage is \(V_m/\pi\), while full-wave rectifier gives \(2V_m/\pi\).

Answer 1

The Correct Option is C

Step 1: Use formula for dc output of half-wave rectifier.
The average (dc) value of output voltage is given by:
\[ V_{dc} = \frac{V_m}{\pi} \]
where \(V_m\) is peak voltage.

Step 2: Substitute given value.
\[ V_m = 33\,\text{V} \]
\[ V_{dc} = \frac{33}{\pi} \]

Step 3: Approximate value of \(\pi\).
\[ \pi \approx 3.14 \]
\[ V_{dc} = \frac{33}{3.14} \]

Step 4: Calculate the value.
\[ V_{dc} \approx 10.5\,\text{V} \]

Step 5: Interpretation.
Only the positive half-cycle contributes in a half-wave rectifier, hence average value is reduced by factor \(\pi\).

Step 6: Final answer.
\[ \boxed{10.5\,\text{V}} \]

Step 7: Concept clarity.
For half-wave rectifier, always remember \(V_{dc} = \frac{V_m}{\pi}\), whereas for full-wave it is \(\frac{2V_m}{\pi}\).