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Question

Acceptor circuit is?


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Solution

Step 1: Derivation of Resonance

The current in a series LCR circuit impressed by an ac emf v=V0cosωt-Φ is given by i=I0cosωt-Φ, where

I0=V0R2+ωL-1ωC2 and Φ=tan-1ωL-1ωCR.

The rms current is Ir=VrR2+ωL-1ωC2

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

ωL=1ωC or ω=1LC=ω0(say).

Step 2: Acceptor Circuit Explanation

  1. This is known as current resonance and ω0 is called the resonant angular frequency.
  2. At resonance Φ=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

13.7: The RLC Series Acceptor Circuit - Physics LibreTexts

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