Obtain the condition for resonance. Draw a plot showing the variation of current with the frequency of a.c. source for two resistances $R_{1}$ and $R_{2}$ ( $R_{1} > R_{2}$ ). Hence define the quality factor, Q and write its role in the tuning of the circuit.

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Solution

The condition at resonance : $X_{L} = X_{C}$
The variation of current with the frequency of a.c. source for two resistances $R_{1}$ and $R_{2}$ where $(R_{1} > R_{2})$ is shown in the figure.
Quality factor is the ratio of voltage drop across the inductor or capacitor to the voltage drop across the resistor.
With increasing Q or quality factor, so the bandwidth of the tuned circuit filter is reduced. As losses decrease so the tuned circuit becomes sharper as energy is stored better in the circuit.It is also use within an oscillator circuit because it is easier to set up and maintain an oscillation as less energy is lost in the tuned circuit.

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