The average value of a full-wave rectified voltage with a peak value of 66 V is: 

Explanation:

Average Value of Full-Wave Rectified Voltage

Definition: The average value of a full-wave rectified voltage is the mean of all the instantaneous values of the rectified voltage over one complete cycle of the input AC signal. It is a measure of the DC component of the rectified output.

Working Principle: In a full-wave rectifier, both the positive and negative halves of the AC signal are converted to positive voltage. This means that the output voltage is always positive, regardless of the input voltage polarity. The average value of this rectified voltage can be determined by integrating the rectified signal over one complete cycle and then dividing by the period of the cycle.

Formula: The average value (V_avg) of a full-wave rectified voltage with a peak value (V_m) can be calculated using the following formula:

V_avg = (2 * V_m) / π

Where:

• V_m is the peak value of the input AC voltage.
• π is a mathematical constant approximately equal to 3.14159.

Calculation:

Given that the peak value (V_m) is 66 V, we can substitute this value into the formula to find the average value:

V_avg = (2 * 66 V) / π

V_avg = 132 V / 3.14159

V_avg ≈ 42 V

Correct Option Analysis:

The correct option is:

Option 2: 42 V

This option correctly represents the average value of the full-wave rectified voltage with a peak value of 66 V, as calculated using the formula for the average value of a full-wave rectified signal.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 66 V

This option incorrectly suggests that the average value is equal to the peak value of the input voltage. However, the average value of a full-wave rectified signal is always less than the peak value. The peak value represents the maximum instantaneous voltage, not the average.

Option 3: 33 V

This option may confuse the average value with half the peak value. However, the correct average value is derived from the formula (2 * V_m) / π, which does not result in half the peak value.

Option 4: 88 V

This option may stem from a misunderstanding of the rectification process. The value 88 V is not related to the average calculation and is not derived from the provided peak value using the correct formula.

Conclusion:

Understanding the calculation of the average value of a full-wave rectified voltage is crucial in analyzing rectifier circuits. The correct average value for a full-wave rectified voltage with a peak value of 66 V is approximately 42 V, as determined by the formula (2 * V_m) / π. This understanding helps in designing and analyzing power supplies and other electronic circuits that utilize rectification to convert AC to DC.