An FM radio tuning circuit has a coil with an inductance of 0.0015 mH.What is the value of the capacitance if the set is tuned to 98 MHz? A) 1.8 × 10−⁶ μF B) 0.88 × 10−⁶ μF C) 0.98 × 10−⁶ μF D) 12 × 10−⁶ μF

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Quizplus · Accepted Answer

The resonant frequency of an LC circuit is given by:$$f = \frac{1}{2\pi\sqrt{LC}}$$where:* f is the resonant frequency in Hz* L is the inductance in henrys* C is the capacitance in faradsWe can rearrange this equation to solve for C:$$C = \frac{1}{4\pi^2f^2L}$$Plugging in the given values, we get:$$C = \frac{1}{4\pi^2(98 	imes 10^6 Hz)^2(0.0015 	imes 10^{-3} H)} = 1.8 	imes 10^{-6} \mu F$$Therefore, the correct answer is A.

An FM Radio Tuning Circuit Has a Coil with an Inductance