## Circuit Analysis ### Circuit Description The circuit is a half-wave rectifier with an input AC voltage source and two diodes. The input voltage is given as: \[ V_i =15 \cos200\pi) \, \text{V \] ###ode Operation **Ideal Diodes**: Assume no forward voltage drop; they conduct perfectly when forward-biased block completely when reverse-biased. ### Operation 1. **Positive Half-Cycle**: - When \( V_i > \), D1 is forward-biased, and D2 is reverse-biased. - The output voltage \( V_o \) across the load resistor is approximately the same as \( V_i \). 2. **Negative Half-Cycle**: - When \( V_i < \), D1 is reverse-biased, and D2 is forward-biased. - The output voltage \( V_o \) across the load is since the diode D2 provides a path to ground. ### Output Voltage - The output voltage \( V_o \) will be a rectified waveform, only showing the positive half-cycles of the input voltage. ### Sketch - **Input Voltage**: A cosine wave oscillating between -15 V and 15 V. - **Output Voltage**: A waveform oscillating between V and 15 V, only during the positive half-cycles of the input. ### Graphical Representation - **Input Voltage (Vi)**: Sinusoidal wave from -15 V to 15 V. - **Output Voltage (Vo)**: Pulsating DC, starting from V, peaking at 15 V during positive half-cycles, dropping to V during negative half-cycles. This analysis assumes ideal behavior for the diodes without considering any real-world imperfections or voltage drops.