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Impedance

In a series L...

Question

In a series LCR circuit connected to an ac source of variable frequency and voltage $v = v_{m} sin ω t$ , draw a plot showing the variation of current $(I)$ with angular frequency $(ω)$ for two different values of resistance $R_{1}$ and $R_{2}$ $(R_{1} > R_{2})$ . Write the condition under which the phenomenon of resonance occurs. For which value of the resistance out of the two curves a sharper resonance is produced? Define Q-factor of the circuit and give its significance.

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Solution

$J_{0} =$ resonance frequency
$f_{0} = \frac{1}{2 π \sqrt{L C}}$
For resistance $R_{2}$ $(R_{2} < R_{1})$ a sharper resonance occur.
$Q$ factor or quality factor define as the ratio of energy stored within the system, higher the value of $Q$ rate of losses lower.

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