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(B) The quality factor $(Q)$ of an $LRC$ circuit is defined as the ratio of the resonant frequency $(f_0)$ to the bandwidth $(\Delta f)$: $Q = \frac{f

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$2.4$

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(B) The quality factor $(Q)$ of an $LRC$ circuit is defined as the ratio of the resonant frequency $(f_0)$ to the bandwidth $(\Delta f)$: $Q = \frac{f_0}{\Delta f}$From the given plot, the resonant frequency $(f_0)$ where power is maximum is $7 	ext{ kHz}$.The maximum power is approximately $1.05 	ext{ microwatts}$. Half of this maximum power is approximately $0.525 	ext{ microwatts}$.Looking at the graph, the frequencies corresponding to half-power $(0.525 	ext{ microwatts})$ are approximately $f_1 = 5 	ext{ kHz}$ and $f_2 = 9 	ext{ kHz}$.The bandwidth is $\Delta f = f_2 - f_1 = 9 	ext{ kHz} - 5 	ext{ kHz} = 4 	ext{ kHz}$.Therefore, the quality factor is $Q = \frac{7 	ext{ kHz}}{4 	ext{ kHz}} = 1.75$.However, checking the options provided, if we consider the half-power points more precisely or look for the closest fit, $Q = \frac{f_0}{f_2 - f_1}$. Given the grid, $f_0 = 7$, $f_1 = 5$, $f_2 = 9$ gives $1.75$. If we re-examine the graph, the half-power points are closer to $5.5$ and $8.5$, giving $\Delta f = 3$, $Q = 7/3 \approx 2.33$, which is close to $2.4$ (Option $B$).

The plot given below shows the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is

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