A series LCR circuit is connected across an a.c. source of variable angular frequency ‘ $straight omega$ ’. Plot a graph showing variation of current 'i' as a function of ‘’ for two resistances R₁ and R₂ (R₁ > R₂).

Answer the following questions using this graph:

(a) In which case is the resonance sharper and why?
(b) In which case in the power dissipation more and why?

Solution

a) The variation of current with angular frequency for the two resistances R₁ and R₂is shown in the graph below:

We can see that the resonance for the resistance R₂ is sharper than for R₁ because resistance R₂is less than resistance R₁. Therefore, at resonance, the value of peak current will rise more abruptly for a lower value of resistance.

b) Power associated with resistance is given by, $P space equals space E subscript V I subscript V$
From the above graph, we can say that virtual current in case of R₂ is more than the virtual current in case of R₁. Therefore, the power dissipation for circuit with R₂is more than that with R₁.

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