Discussion
A parallel circuit has R = 1kΩ, C= 50µF and L = 10mH. The quality factor at resonance is ________.
Answer: C
The quality factor is about 70.70.
For a parallel resonant circuit with resistance R in parallel with L and C, the quality factor is \(Q = R\sqrt{C/L}\).
\[ \begin{aligned} Q &= 1000\sqrt{\frac{50 \times 10^{-6}}{10 \times 10^{-3}}} \\ &= 1000 \times \sqrt{5 \times 10^{-3}} \\ &= 1000 \times 0.0707 = 70.7 \end{aligned} \]
Using the series formula \(\frac{1}{R}\sqrt{L/C}\) would give a tiny value, and 100, 90.86 and 78.76 do not follow from these component values.
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