The circuit above consists of an a. c. voltage input, a diode, a resistor and a voltmeter. (a) Identify the circuit. (b) Draw the waveform for the output vo...

Answer Details

(a) Identification of the circuit

An a.c. supply feeding a single diode in series with a load resistor, with a voltmeter connected across the resistor, is a half-wave rectifier. The diode conducts only when it is forward-biased. During the positive half-cycle of the a.c. input the diode conducts and the current passes through the resistor, so the input voltage appears across it. During the negative half-cycle the diode is reverse-biased and blocks the current, so the output falls to zero. Only one half of every complete a.c. cycle therefore reaches the load, which is why the arrangement is called a half-wave rectifier.

(b) Waveform for the output voltage

The output consists of the positive half-cycles only. During each positive half-cycle the voltage follows the sine curve of the input, rising to a peak value \(V_{p}\) and returning to zero; during each negative half-cycle the diode does not conduct, so the output stays at zero, leaving a flat gap before the next positive hump appears. The graph below shows the sinusoidal a.c. input (dashed) together with the resulting half-wave rectified output (solid) over two complete cycles.

Key features of the output waveform:

• It is a series of separated positive half-sine humps (the negative half-cycles are removed).
• The peak of each hump equals the peak input voltage \(V_{p}\).
• Between successive humps the output is zero for a full half-cycle.
• The output is a pulsating d.c. (unidirectional) voltage with the same period as the a.c. input.