Question

Acceptor circuit is?

Answer 1

Step 1: Derivation of Resonance

The current in a series LCR circuit impressed by an ac emf $v=V_0\cos \left(\omega t-\Phi \right)$ is given by $i=I_0\cos \left(\omega t-\Phi \right)$, where

$I_0=\frac{V_0}{\sqrt{R^2+{\left(\omega L-{\displaystyle \frac{1}{\omega C}}\right)}^2}}$ and $\Phi ={\tan }^{-1}\frac{\omega L-{\displaystyle \frac{1}{\omega C}}}{R}$.

The rms current is $I_r=\frac{V_r}{\sqrt{R^2+{\left(\omega L-{\displaystyle \frac{1}{\omega C}}\right)}^2}}$

where $V_r$ is the rms voltage. Thus $I_r$ depends on the frequency $\omega$ of the impressed ac emf. For a certain value of $\omega$, $I_r$ becomes maximum and we say there is resonance. If $I_r$ is plotted as a function of $\omega$ we get a curve like that shown in the figure. Obviously the current $I_r$ attain a maximum value when

$\omega L=\frac{1}{\omega C}$ or $\omega =\frac{1}{\sqrt{LC}}={\omega }_0$(say).

Step 2: Acceptor Circuit Explanation

1. This is known as current resonance and ${\omega }_0$ is called the resonant angular frequency.
2. At resonance $\Phi =0$, i.e., current and voltage are in phase.
3. As the current response of the circuit is maximum at resonance the series LCR circuit is sometimes called an acceptor circuit.
4. If the input consists of a number of frequency components the circuit will have a good response only for frequencies near the resonant frequency.
5. The circuit has thus, selective properties.
6. It can be used as a filter to select a narrow band of frequencies about resonant frequency.

Step 3: A diagram to represent the acceptor circuit