Step 1: Understanding the Concept:
A diode only allows current to flow when it is forward-biased. When we measure voltage across the diode in a series circuit, we are seeing the portions of the input signal that the diode "blocks" or "drops."
Step 2: Detailed Explanation:
1. Forward Bias (Positive Half Cycle): If the diode is forward-biased, it acts like a closed switch (short circuit). Ideally, the voltage drop across a short circuit is zero.
2. Reverse Bias (Negative Half Cycle): The diode acts like an open switch. No current flows through the resistor $R$, so the entire input voltage appears across the diode.
3. Consequently, the output waveform measured across the diode shows the negative halves of the AC cycle while remaining zero during the positive halves.
Step 3: Final Answer:
The voltage across the diode will show the waveforms of the blocked half-cycles (Option 3).