To find the average value of a full-wave rectified voltage whose peak value is 42 V, we can use the formula for the average value of the full-wave rectified sine wave.
1. Understanding the Full-Wave Rectification:
In full-wave rectification, both the positive and negative halves of the AC waveform are converted to a DC waveform. The rectified output won't have any negative portions; it will be all positive portions of the sine wave.
2. Formula:
The formula for the average value [tex]\( V_{avg} \)[/tex] of a full-wave rectified voltage is given by:
[tex]\[
V_{avg} = \frac{2 \cdot V_m}{\pi}
\][/tex]
where [tex]\( V_m \)[/tex] is the peak value of the voltage.
3. Given:
The peak value [tex]\( V_m \)[/tex] is [tex]\( 42 \, V \)[/tex].
4. Substitution:
Substituting [tex]\( V_m = 42 \, V \)[/tex] into the formula, we get:
[tex]\[
V_{avg} = \frac{2 \cdot 42}{\pi}
\][/tex]
5. Calculation:
Carry out the division and multiplication to find the value:
[tex]\[
V_{avg} = \frac{84}{\pi}
\][/tex]
When we compute this, the numerical value approximately comes out to:
[tex]\[
V_{avg} \approx 26.738 \, V
\][/tex]
So, the average value of the full-wave rectified voltage with a peak value of 42 V is approximately [tex]\( 26.738 \, V \)[/tex].
