Question

In half wave rectifiers a p-n diode with internal resistance $20\Omega$is used. If the load resistance of $2k\Omega$ is used in the circuit, then find the efficiency of this half wave rectifier.

Answer 1

Hint It is given that a P-N junction diode has an internal resistance of $20\Omega$ and there is a load resistance given. Directly substitute the values in the efficiency of the half wave rectifier formula and calculate the percentage value.

Complete Step By Step Solution
A Half wave rectifier is a type of rectifier which is tuned to allow only one half cycle of alternating transformation wave to pass and block the other half , which converts one half AC voltage into DC voltage. This rectifier requires only one single diode to achieve this operation.
Rectifier efficiency is defined as the ratio of the amount of DC power obtained by the AC input voltage given. It is mathematically given as ,
$\eta = {P_{dc}}/{P_{ac}} = \dfrac{{0.406{R_L}}}{{{r_f} + {R_L}}}$
Where ${R_L}$is load resistance value and ${r_f}$is the internal resistance value of the diode. In our given question, ${r_f}$is said to have a resistance of $20\Omega$ and Load resistance of $2k\Omega$. Substituting the values in the above formula we get,
$\Rightarrow \eta = \dfrac{{0.406(2 \times {{10}^3})}}{{(20 + 2 \times {{10}^3})}}$
Further simplifying we get,
$\Rightarrow \eta = \dfrac{{812}}{{2020}}$
$\Rightarrow \eta = 0.401$
Taking the percentage value, we get
$\Rightarrow \eta = 40.1\%$

Therefore the efficiency of the given half wave rectifier is $40.1\%$.

Note
A rectifier is a device that is predominantly used to convert alternating current that reverses its direction in periods , to DC current, that is a straight flow of current. A rectifier circuit requires a set of p-n junction diodes based upon the rectification scale. There are two types of rectifier namely, half wave rectifier and full wave rectifier. A full wave rectifier consists of two power diodes that are connected to a single load resistance, with each diode functioning in each periodic cycle of the alternating current.