Question 6A102

The resonant frequency ($f_r$) of a parallel LC circuit is determined by the formula: $f_r = \frac{1}{2\pi\sqrt{LC}}$. In this scenario, the initial resonant frequency is 1000 kHz. The problem states that L and C are varied, but their *product* (LC) remains constant. Since $2\pi$ is a mathematical constant and the product LC remains constant, the entire denominator ($2\pi\sqrt{LC}$) of the resonant frequency formula remains unchanged. Consequently, if the denominator is constant, the resonant frequency itself must also remain constant. Therefore, the resulting resonant frequency will be the same as the original frequency. 1000 kHz is equivalent to 1 MHz. Thus, the resonant frequency remains 1 MHz.