Problem 58-3    Source:   Example 20.5 - pag.e 614 - BOYLESTAD, Robert L. - Book: Introdução à Análise de Circuitos - 10ª ed. - 2008.

A series RLC circuit is designed to resonate at ω_S = 10⁵ rad/s, with a bandwidth of 0.15 ω_S, and consumes 16 watts from a source of 120 volts in the resonance.

a) Determine the value of R.

b) Calculate the bandwidth in hertz.

c) Calculate the nominal values of L and C.

d) Which is Q_S of circuit.

e) Determine the relative bandwidth.

Solution of the Problem 58-3   

Item a

Since the circuit is in resonance, it is known that the impedance of the circuit is equal to R. Then:

Item b

The problem statement already says that the bandwidth is 15% of the resonant frequency. Calculating how much it is 15% of 10⁵ rad/s.

As the statement asks for the result in hertz, transforming:

Item c

Knowing the bandwidth and the value of R we can calculate the value of L, or:

In order to calculate the value of C, we use the equation that allows us to calculate the frequency of resonance, that is, the eq. 57-3. Not forgetting that ω = 2 π f:

Item d

Item e

The relative band is given by: