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Which of the following combinations should be selected for better tuning of an LCR a.c. circuit used for communication?

Asked in GSEB Board March 2023 · Resonance condition and tuning

• (1) R=15 Ω, L=3.5 H, C=30 μF
• (2) R=25 Ω, L=2.5 H, C=45 μF
• (3) R=20 Ω, L=1.5 H, C=35 μF
• (4) R=25 Ω, L=1.5 H, C=45 μF

Step-by-step solution

Why the other options are wrong

• (2) Here Q=1/(25)√(2.5)/(45×10⁻⁶)≈9.4, less than half of the first set's 22.8. Its larger R and larger C both flatten the resonance.
• (3) Here Q=1/(20)√(1.5)/(35×10⁻⁶)≈10.4. Its smaller L and larger R make the resonance less than half as sharp as the first set's (22.8).
• (4) Here Q=1/(25)√(1.5)/(45×10⁻⁶)≈7.3, the worst of the four: the largest R, the smallest L and the largest C all lower Q.

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