WAEC Physics 2010 Paper

Concept:The resonant frequency of an a.c circuit depends on the inductance and capacitance and is given by $f = \frac{1}{2\pi\sqrt{LC}}$.Explanation:When both $L$ and $C$ are reduced by $50\%$, the new values are $L' = \frac{L}{2}$ and $C' = \frac{C}{2}$.The new product becomes $L'C' = \frac{L}{2} \times \frac{C}{2} = \frac{LC}{4}$.Substitute this product into the formula: $f' = \frac{1}{2\pi\sqrt{LC/4}}$.Since $\sqrt{LC/4} = \frac{1}{2}\sqrt{LC}$, the expression simplifies to $f' = \frac{2}{2\pi\sqrt{LC}} = 2f$.Thus, reducing both $L$ and $C$ by half doubles the resonant frequency.Given $f = 1000\text{ kHz}$, the new resonant frequency is $f' = 2(1000) = 2000\text{ kHz}$.Answer:D. $2000\text{ kHz}$