A full wave pn-junction diode rectifier uses a load resistance of 1200 Ω. The internal resistance of each diode is 9 Ω. Find efficiency.

Steps to Solve

1. Calculate Total Resistance

First, determine the total resistance of the circuit. In a full-wave rectifier, two diodes conduct at the same time, so their internal resistances add up: $$ R_{total} = R_{load} + 2 \times R_{diode} $$ Here, $R_{load} = 1200 , \Omega$ and $R_{diode} = 9 , \Omega$.

2. Substitute Values

Now, substitute the values into the equation: $$ R_{total} = 1200 + 2 \times 9 $$ Calculating this gives: $$ R_{total} = 1200 + 18 = 1218 , \Omega $$

3. Calculate Efficiency

The efficiency ($\eta$) of a rectifier is given by the formula: $$ \eta = \frac{R_{load}}{R_{total}} \times 100% $$ Substituting the values: $$ \eta = \frac{1200}{1218} \times 100% $$

4. Perform the Calculation

Now calculate the efficiency: $$ \eta \approx 0.9851 \times 100% \approx 98.51% $$