MHTCET 26 Apr 2025 Shift 2 Paper

Concept:Find the equivalent inductance and capacitance from the given circuit, then use the LC resonance frequency formula.Explanation:The two inductors, each of inductance $L$, are connected in parallel.For parallel inductors: $\frac{1}{L_T} = \frac{1}{L} + \frac{1}{L} = \frac{2}{L}$.Thus, $L_T = \frac{L}{2}$.The two capacitors, each of capacitance $C$, are connected in series.For series capacitors: $\frac{1}{C_T} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C}$.Thus, $C_T = \frac{C}{2}$.The resonant frequency of an LC circuit is given by:$f = \frac{1}{2\pi\sqrt{L_T C_T}}$.Substituting the equivalent values:$f = \frac{1}{2\pi\sqrt{\frac{L}{2} \cdot \frac{C}{2}}} = \frac{1}{2\pi\sqrt{\frac{LC}{4}}}$.This simplifies to:$f = \frac{1}{\pi\sqrt{LC}}$.Answer:Option C: $\frac{1}{\pi\sqrt{LC}}$.