Peak Output Voltage of a Full-Wave Rectifier

A full-wave rectifier is a device that converts an alternating current (AC) input voltage into a direct current (DC) output voltage. It is commonly used in power supplies and electronic circuits to convert AC power to DC power.

When an AC signal is applied to a full-wave rectifier, it produces a pulsating DC waveform. The peak output voltage of the rectifier refers to the maximum voltage that is reached during each cycle of the AC input signal.

Calculating the DC Voltage

To calculate the DC voltage of the full-wave rectifier, we need to determine the average or mean value of the rectified waveform. This can be done by taking the average of the positive half cycles of the waveform.

The peak output voltage of the full-wave rectifier is given as 10V. Let's assume the voltage across the load resistor during each positive half cycle is Vp (peak voltage). The average value of the rectified waveform can be calculated using the following formula:

Vdc = (2 * Vp) / π

Where:
- Vdc is the DC voltage
- Vp is the peak voltage

Deriving the Formula

The formula for calculating the average value of a rectified waveform can be derived using the concept of the Fourier series. The Fourier series expansion of a rectified waveform consists of only odd harmonics. By considering the first harmonic, we can determine the average value of the waveform.

For a full-wave rectifier, the first harmonic is given by:

V1 = (4 * Vp) / π

The average value of the rectified waveform is then:

Vavg = (2 * V1) / π
= (2 * (4 * Vp) / π) / π
= (8 * Vp) / π^2

Since the DC voltage is the average value of the rectified waveform, we can rewrite the formula as:

Vdc = (8 * Vp) / π^2

By substituting the given peak output voltage of 10V, we get:

Vdc = (8 * 10) / π^2
≈ 6.36V

Therefore, the DC voltage of the full-wave rectifier is approximately 6.36V.