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The resonance frequency of an LCR series A.C. circuit is f₀. Now the capacitance is made 4 times; then the new resonance frequency will become

Asked in GUJCET 2007 · Resonance condition and tuning

• (1) (f₀)/4
• (2) 2f₀
• (3) f₀
• (4) (f₀)/2

Step-by-step solution

Why the other options are wrong

• (1) (f₀)/4 treats f₀ as inversely proportional to C itself. The formula has √C, so making C four times changes f₀ by only √4=2.
• (2) 2f₀ has the dependence upside down: f₀∝1/(√C), so a larger capacitance lowers the resonant frequency.
• (3) The resonant frequency is set by L and C, so changing C must change it.

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