GATE EC 2023 Set 1 — Question 18
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Network Theory → Transient & AC Analysis → Quality Factor & Bandwidth
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Question
A series RLC circuit has a quality factor of 1000 at a center frequency of rad/s. The possible values of , and are
Correct answer
(D) R = 0.001 Ω, L = 1 μ H and C = 1 μ F
Solution
For a series RLC circuit, the resonant frequency and the quality factor are given by:Given:
rad/sLet's check each option:Option (A):
rad/s (Matches)
(Does not match )Option (B):
rad/s (Matches, as L and C are the same as in A)
(Does not match )Option (C):
rad/s (Matches)
(Does not match )Option (D):
rad/s (Matches)
(Matches)Thus, option (D) provides the correct values for , , and that satisfy the given quality factor and center frequency.The final answer is
rad/sLet's check each option:Option (A):
rad/s (Matches)
(Does not match )Option (B):
rad/s (Matches, as L and C are the same as in A)
(Does not match )Option (C):
rad/s (Matches)
(Does not match )Option (D):
rad/s (Matches)
(Matches)Thus, option (D) provides the correct values for , , and that satisfy the given quality factor and center frequency.The final answer is
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