In an ideal half-wave rectifier with zero mean sine wave input, the output is

Explanation:

Ideal Half-Wave Rectifier

Definition: A half-wave rectifier is an electronic circuit that converts an alternating current (AC) input signal into a pulsating direct current (DC) output signal. It achieves this by allowing current to flow through the load only during one half-cycle of the input AC waveform, while blocking the current during the other half-cycle. This operation is typically achieved using a single diode in the circuit.

Working Principle: In a half-wave rectifier, the diode is forward-biased during one half of the AC cycle (positive half-cycle for a typical configuration), allowing current to pass through. During the other half of the AC cycle (negative half-cycle), the diode becomes reverse-biased and blocks the current. As a result, the output voltage is non-zero only during one half of the AC input cycle and zero during the other half.

Correct Option Analysis:

The correct option is:

Option 1: Non-zero during only one half cycle of input.

This option is correct because the primary characteristic of an ideal half-wave rectifier is that it allows current to flow through the load only during one half of the AC input cycle. For a zero mean sine wave input, this means the rectifier will produce a pulsating output that corresponds to the positive or negative half-cycles of the input waveform, depending on the orientation of the diode. The output will remain zero during the other half-cycle when the diode is reverse-biased.

Mathematical Analysis:

Let the input AC signal be represented as:

v_in(t) = V_msin(ωt), where:

• V_m = Peak amplitude of the sine wave.
• ω = Angular frequency of the AC signal.

During the positive half-cycle of the input (0 ≤ ωt ≤ π), the diode is forward-biased, and the output voltage is:

v_out(t) = V_msin(ωt)

During the negative half-cycle of the input (π ≤ ωt ≤ 2π), the diode is reverse-biased, and the output voltage is:

v_out(t) = 0

Thus, the output of an ideal half-wave rectifier is non-zero only during one half-cycle of the input AC signal