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# The Q factor of an ac circuit lies between:A. $0$ and $1$B. $- 1$ and $1$C. $- 1$ and $0$D. None of these

Last updated date: 22nd Jul 2024
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Hint: The Q factor in an AC circuit is the ratio of energy stored in the capacitor to energy lost as thermal losses in the equivalent series resistance. The Q factor does not have a fixed value. For two factors, it varies greatly with frequency.

Complete step-by-step solution:
The capacitor's Q factor, also known as the quality factor or simply Q, is a measurement of the capacitor's performance in terms of energy losses. It is defined as follows:
${Q_c} = \dfrac{{{X_c}}}{{{R_c}}} = \dfrac{1}{{{\omega _o}C{R_c}}}$
Where ${Q_c}$is the quality factor, ${X_c}$is the capacitor's reactance,$\;C$ is the capacitor's capacitance, ${R_c}$is the capacitor's corresponding series resistance (ESR), and $0$ is the measurement frequency in radians.
Q factor varies $0 < Q < \infty$
$Q = 1$ Critical damp
$Q < 1$ Underdamp
$Q > 1$ Over damp
Let us get some ideas about damping a circuit.
The RLC circuit damping has an impact on how the voltage response achieves its final (or steady state) value.
When ${\left( {\dfrac{R}{{2L}}} \right)^2} > \dfrac{1}{{LC}}$ that refers to the case where the circuit is said to be over-damped and has two real roots.
When ${\left( {\dfrac{R}{{2L}}} \right)^2} < \dfrac{1}{{LC}}$ This refers to the situation where the circuit is said to be under-damped and has two complex roots (as root( -1) is imaginary).
When ${\left( {\dfrac{R}{{2L}}} \right)^2} = \dfrac{1}{{LC}}$ This refers to the situation where the circuit is said to be critically damped since the two roots of the equation are identical (i.e. there is only one root).

Note: So, back when radio was new, in the 19th and 20th centuries, to hear communication at a specific frequency, you had to tune into it, adjust the inductor value, and try to get a high "Q factor" at that frequency of communication, so that you could hear it clearly, i.e. to have high "Quality" communication. And we continue to use this definition because, why not, it is extremely useful. And it was with this in mind that the Q-factor was introduced.