Full Wave Rectifier: CBSE Class 12 Physics Marking Scheme
Step 1 (Working Principle): [1 Mark]
The working principle of a full-wave rectifier is based on the unidirectional property of the $p-n$ junction diode. It converts both halves of the input AC cycle into a unidirectional DC output. During the positive half-cycle, one diode is forward-biased and conducts, while during the negative half-cycle, the other diode is forward-biased and conducts, ensuring current flows through the load resistor $R_L$ in the same direction for both cycles.
Step 2 (Circuit Diagram & Waveforms): [1 Mark]
Note: In the examination, ensure the center-tapped transformer is clearly labeled with diodes $D_1$ and $D_2$.
Circuit Diagram Description:
- Input AC is applied to the primary coil of a center-tapped transformer.
- Two diodes $D_1$ and $D_2$ are connected to the ends of the secondary coil.
- The load resistor $R_L$ is connected between the center tap and the common junction of the diodes.
Input-Output Waveforms:
- Input: A continuous sinusoidal wave $V_{in} = V_m \sin(\omega t)$.
- Output: A pulsating DC wave where the negative half-cycles are inverted to become positive, resulting in a frequency $f_{out} = 2f_{in}$.
Step 3 (Mathematical Deduction & Conclusion): [1 Mark]
The output voltage across the load $R_L$ is derived from the rectification process. Since the current flows through $R_L$ in the same direction for both half-cycles, the average DC output voltage ($V_{dc}$) is given by:
$$V_{dc} = \frac{2V_m}{\pi}$$Where:
- $V_m$ is the peak value of the secondary voltage.
- The efficiency of a full-wave rectifier is higher than a half-wave rectifier, with a maximum theoretical efficiency of approximately $81.2\%$.
💡 EL10 Concept Insight: Think of a full-wave rectifier like a traffic roundabout that forces cars coming from two different directions to always exit onto the same highway. By using two diodes and a center-tapped transformer, we "flip" the negative part of the electricity wave so it points the same way as the positive part, making the power flow much smoother and more efficient!