Compare features of p-type and n-type semiconductors. Draw circuit diagram of half-wave rectifier of p-n junction diode and explain it.
Explanation of Half-Wave Rectifier:
1. Working Principle: A half-wave rectifier converts AC voltage into pulsating DC using a single p-n junction diode.
2. Positive Half Cycle: During the positive half-cycle of AC input, the diode is forward biased and allows current to flow through the load resistor (\( R_L \)).
3. Negative Half Cycle: During the negative half-cycle, the diode is reverse biased and blocks current flow, resulting in no output.
4. Output Waveform: The output consists of only the positive half-cycles of the AC input, producing a pulsating DC voltage.
Explain the operation of p-n junction diode in forward bias.
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $