An LC circuit with L = 40 mH is used in a radio to determine thefrequency of a s

Question

An LC circuit with L = 40 mH is used in a radio to determine thefrequency of a selected radio station. The station's frequency isequal to the resonant frequency of the circuit. (a) The radio is initially set for a frequencyf = 0.94 MHz. What is thevalue of C?
1 F

(b) This capacitance is then increased by 40%. What is the new resonant frequency?
2 MHz
(a) The radio is initially set for a frequencyf = 0.94 MHz. What is thevalue of C?
1 F

(b) This capacitance is then increased by 40%. What is the new resonant frequency?
2 MHz

Explanation / Answer

given that L = 40mH = 40 * 10-3H f = 0.94MHZ = 0.94 * 106 HZ    resonant frequency = f= 1/2LC                             C = 1/f2 (42)L plug in values = C = 1/(0.94 *106)2 (4* 3.142) * 40 *10-3                          C = 0.72 * 10-12 F if the capacitence is incresed by 40% then new capacitence = C1= (0.72 +0.4 *0.72)                                         = 1.008 * 10-12F then new resonant frequency = f=1/2LC1       plug in values                                          = -----------MHZ       plug in values                                          = -----------MHZ

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