Question 122: AC fundamentals

Question

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.

Accepted Answer

Quality factor = $${{{X_L}} \over R} = {{\omega L} \over R}$$
$$Q = {1 \over {\sqrt {LC} }}{L \over R}$$
$$Q = \left( {{1 \over {\sqrt C }}} \right){{\sqrt L } \over R}$$
$$Q = {{XL} \over R} = {{\omega L} \over R} = {1 \over {\sqrt {LC} }}{L \over R} = {1 \over R}{{\sqrt L } \over {\sqrt C }}$$
$$Q' = {{\sqrt {2L} } \over {\left( {{R \over 2}} \right)\sqrt C }} = 2\sqrt 2 Q$$
Q' = 282.84

AC fundamentals

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.

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