You have an AC source that puts out a maximum of 12V at a frequency of 104.3 MHz

Question

You have an AC source that puts out a maximum of 12V at a frequency of 104.3 MHz. The voltage, naturally, follows the form of: ?(t)= ?0 cos(?t). You have a resistor (R = 35?), an inductor (L = 50H) and a variable capacitor.

1.  If you want to tune the radio so that the resonance is on the station with a frequency of 104.3MHz, what value should your capacitor have?

2.  What are the resistance, the capacitive reactance, inductive reactance and the total impedance of the circuit?

3. What is the peak current through the circuit?

4. What is max voltage across each element, R, L, and C?

5. What is the phase angle between current and applied EMF?

Explanation / Answer

here,

volatge , V = 12 V

frequency , f = 104.3 MHz

f = 104.3 * 10^6 Hz

R = 35 ohm

L = 50 H

1.

let the capacitance be C

resonance frequency , f = 1/(2*pi*sqrt(L*C))

104.3 * 10^6 = 1/(2*pi*sqrt(50 *C))

C = 4.66 *10^-20 F

the capacitance is 4.66 *10^-20 F

2.

resistance is 35 ohm

the capacitative reactance , Xc = 1/(2*pi*f*C)

Xc = 1/(2*pi*104.3 * 10^-6*4.66 * 10^-20)

Xc = 3.27 * 10^22 ohm

the inductive reactance , Xl = 2*pi*f*L

Xl = 2*pi*104.3*10^6*50

Xl = 3.28 * 10^10 ohm

3.

impedance , Z = sqrt( R^2 + (Xl - Xc)^2)

Z = sqrt( 35^2 + (3.28 * 10^10 + 3.27 * 10^22)^2)

Z = 3.27 * 10^22 ohm

peak current , I = V/Z

I = 12 / 3.27 * 10^22

I = 3.67 * 10^-22 A

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