What will be the bandwidth of a series resonant circuit provided
A. 1 kHz
B. 10 kHz
C. 1 MHz
D. 0.1 kHz
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
RLC series circuit:
An RLC circuit is an electrical circuit consisting of Inductor (L), Capacitor (C), Resistor (R) it can be connected either parallel or series.
When the RLC circuit is set to resonate (XL = XC), the resonant frequency is expressed as
\(f = \frac{1}{{2π }}\sqrt {\frac{1}{{LC}}}\)
Quality factor:
The quality factor Q is defined as the ratio of the resonant frequency to the bandwidth.
\(Q=\frac{{{f}_{r}}}{BW}\)
Mathematically, for a coil, the quality factor is given by:
\(Q=\frac{{{\omega }_{0}}L}{R}=\frac{1}{R}\sqrt{\frac{L}{C}}\)
Where,
XL & XC = Impedance of inductor and capacitor respectively
L, R & C = Inductance, resistance, and capacitance respectively
fr = frequency
ω0 = angular resonance frequency
Calculation:
Given that, XL = 1000 Ω
XC = 1000 Ω
R = 0.1 Ω
F0 = 10 MHz
\(\begin{array}{l} Q = \frac{{\omega L}}{R} = \frac{{1000}}{{0.1}} = {10^4}\\ Bandwidth\;\left( {B.\;W} \right) = \frac{{{f_0}}}{Q} = \frac{{10 \times {{10}^6}}}{{{{10}^4}}} = 1\;KHz \end{array}\)