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For a series LCR circuit with L=2 H, C=18 μF and R=10 Ω, what is the value of the Q-factor of this circuit?

Asked in GUJCET 2021 · Power and bandwidth at resonance

• (1) 22.22
• (2) 55.55
• (3) 44.44
• (4) 33.33

Step-by-step solution

Why the other options are wrong

• (1) No single slip produces 22.22. Sanity check: √L/C=√2/(18×10⁻⁶)=333.3 Ω, and dividing by R=10 Ω gives 33.33.
• (2) No single slip produces 55.55. Sanity check: ω₀=1/(√LC)=166.7 rad s⁻¹ and Q=(ω₀L)/R=(166.7×2)/(10)=33.33.
• (3) No single slip produces 44.44. Sanity check: Q=1/R√L/C=(333.3)/(10)=33.33.

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