Choose the correct waveform that can represent the voltage across $$R$$ of the following circuit, assuming the diode is ideal one:

1. Circuit Parameters

• Input Voltage: $$v_i = 10 \sin(\omega t)$$
• Diode ($$D$$): Ideal, pointing to the right (forward-biased when Anode potential $$V_A >$$ Cathode potential $$V_K$$).
• DC Battery Reference: $$+3\text{ V}$$ (positive terminal facing upward toward the resistor).

2. Operational States of the Circuit

Case A: When $$v_i > 3\text{ V}$$ (Diode is ON)

When the input signal rises above the reference battery voltage ($$+3\text{ V}$$), the diode becomes forward-biased and acts as a short circuit (closed switch).

Applying Kirchhoff's Voltage Law (KVL) around the conducting loop:

$$v_i - V_R - 3 = 0 \implies V_R = v_i - 3$$

• The waveform across the resistor tracks the input voltage but is shifted down by $$3\text{ V}$$.
• At the positive peak ($$v_i = +10\text{ V}$$), the output voltage reaches maximum:

  $$V_R = 10 - 3 = +7\text{ V}$$

Case B: When $$v_i \le 3\text{ V}$$ (Diode is OFF)

When the input voltage drops below or equals the reference battery level ($$\le +3\text{ V}$$), the diode is reverse-biased and acts as an open circuit (open switch).

• With the loop broken, zero current flows through the circuit ($$I = 0$$).
• Therefore, the output voltage across the resistor drops flat to baseline:

  $$V_R = 0\text{ V}$$

3. Waveform Identification

The resulting voltage waveform across the load resistor ($$V_R$$) must satisfy two visual rules:

1. It stays perfectly flat at **$$0\text{ V}$$** for any input voltage value below $$+3\text{ V}$$ (clipping the entire negative half-cycle and parts of the positive half-cycle).
2. It projects a smooth sinusoidal peak reaching up to **$$+7\text{ V}$$** only when the input waveform crosses above the $$+3\text{ V}$$ reference threshold.

This exact profile—clipping flat at $$0\text{ V}$$ and tracking only the upper peak relative to the shifted reference axis—corresponds to the first choice on the page layout.

Correct Option: A