**Efficiency of Half Wave Rectifier**

A half wave rectifier is a circuit that converts an AC (alternating current) input voltage into a DC (direct current) output voltage. It uses a p-n junction diode to rectify the input waveform. The efficiency of a half wave rectifier is a measure of how effectively it converts the input power to the output power.

**Efficiency Formula**
Efficiency is defined as the ratio of output power to the input power. Mathematically, it can be expressed as:

Efficiency = (DC power output / AC power input) * 100%

**Calculation of DC Power Output**
The DC power output can be calculated using the formula:

DC power output = (Vrms / RL)^2 * RL

Where:
- Vrms is the root mean square value of the rectified voltage.
- RL is the load resistance.

**Calculation of AC Power Input**
The AC power input can be calculated using the formula:

AC power input = (Vrms / RL + Rd)^2 * (RL + Rd)

Where:
- Vrms is the root mean square value of the input voltage.
- RL is the load resistance.
- Rd is the internal resistance of the diode.

**Calculation of Efficiency**
Substituting the values into the efficiency formula, we get:

Efficiency = [(Vrms / RL)^2 * RL] / [(Vrms / RL + Rd)^2 * (RL + Rd)] * 100%

**Efficiency Calculation Example**
Let's consider an example where the root mean square value of the input voltage (Vrms) is 10V, the load resistance (RL) is 2 ohm, and the internal resistance of the diode (Rd) is 20 ohm.

Efficiency = [(10 / 2)^2 * 2] / [(10 / 2 + 20)^2 * (2 + 20)] * 100%
Efficiency = (25 * 2) / (60 * 22) * 100%
Efficiency = 0.056818 * 100%
Efficiency = 5.68%

Therefore, the efficiency of the given half wave rectifier circuit is approximately 5.68%.

**Explanation**
The efficiency of a half wave rectifier is generally low due to the voltage drop across the diode's internal resistance. In this case, the internal resistance of the diode (20 ohm) significantly affects the efficiency. The load resistance (2 ohm) is relatively low compared to the internal resistance, causing a considerable voltage drop across the diode.

To improve the efficiency of the rectifier, it is important to minimize the internal resistance of the diode and choose an appropriate load resistance. Lowering the internal resistance and increasing the load resistance will decrease the voltage drop across the diode and maximize the output power.

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