Show all work a radio tuner has a 400 ohm resistor, .5 mH inductor, and a capaci

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a radio tuner has a 400 ohm resistor, .5 mH inductor, and a capacitor with capacitance of 72 pF. They are connected in series. Find the resonance and frequency for the circuit. find the reactance of the inductor and capacitor at resonant frequency. Show all work
a radio tuner has a 400 ohm resistor, .5 mH inductor, and a capacitor with capacitance of 72 pF. They are connected in series. Find the resonance and frequency for the circuit. find the reactance of the inductor and capacitor at resonant frequency. Show all work
a radio tuner has a 400 ohm resistor, .5 mH inductor, and a capacitor with capacitance of 72 pF. They are connected in series. Find the resonance and frequency for the circuit. find the reactance of the inductor and capacitor at resonant frequency.

Explanation / Answer

As given in the question,

Resistance: R = 400

Capacitance: C = 72 pF = 72*10^-12 F

Inductance: L = 5 mH = 5*10^-3 H

(a) For the resonance frequency condition,

XC  = XL

=> 1 / (w*C) = w*L

=>   w  = 1 / sqrt[L*C]

   = 1 / sqrt[(5*10^-3)*(72*10^-12)] = 1.67*10^6 rad/s

So, the resonant frequency:

f  = w / 2  = (1.67*10^6) / 2 = 2.65*10^5 Hz

(b)   At this resonant frequency condition,

Reactance of the inductor:   XL  = w*L  = (1.67*10^6)*(5*10^-3) = 3.34*10^8

Reactance of the capacitor:   XC  = 1 / w*C = 1 / (1.67*10^6)*(72*10^-12) = 8.32*10^3

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