Problem 58-5    Source:   problem 6 - page 355 - BARTKOWIAK, Robert A. - Book: Circuitos Elétricos - 2ª ed. - Editora Makron Books - 1999.

The antenna circuit of a radio receiver consists of a serial connection of a coil of 10 mH, a variable capacitor, and a 50 ohm resistor. A signal of 880 KHz produces a potential difference of 100 µ V on the resonance. Find:

a) The current in the resonance.

b) The value of capacitance at resonance.

c) Determine the Q of the antenna circuit.

Solution of the Problem 58-5   

Item a   

For the radio receiver to tune the frequency of 880 KHz the series circuit should be in resonance. In this way the reactances cancel out and the impedance of the circuit is the value R = 50 ohms. Then the current in the resonance of the circuit is:

Item b   

Manipulando algebricamente a eq. 58-04, encontra-se o valor de C, ou:

Substituting the numerical values and performing the calculation:

Item c   

For the calculation of Q will be used the eq. 58-09. For this it is necessary to calculate the value of X_L. Then:

Then the value of Q is: