Bandwidth Formula RLC circuit

By Varadi Hema|Updated : July 29th, 2022

A series circuit has a bandwidth of 300 rad/sec at a resonant frequency of 3000 rad/sec when excited by a voltage source of 100 V. the inductance of the coil is 0.1 H. the value of R and the voltage across C is, respectively.
A. 10 ohms, 100 V
B. 30 ohms, 100 V
C. 30 ohms, 1000 V
D. 300 ohms, 1000 V

Answer: 30 ohms, 1000 V

The bandwidth formula for the series rlc circuit is B.W=R/L.


Bandwidth is generally defined as a band of frequencies a circuit passes or rejects. 

The bandwidth of the rlc circuit is defined as the range of frequencies for which circuit output voltage (or) current value equals 70.7 % of its maximum amplitude, which will occur at the resonant frequency.

The bandwidth formula for the series rlc circuit is B.W=R/L

Given data,

Resonant frequency ωr=3000 rad/sec,

Excitation (or) input voltage V=100 V,

Bandwidth B.W=300 rad/sec,

Inductance L=0.1 H,

As we know, B.W=RL=300 rad/sec

Then R=300×0.1=30

Under resonant condition XL=XC


C=1/ω2L=1/(30002.(0.1))=1.111 μF

Current through series resonant circuit I=V/Z=V/R=100/30 =10/3

And voltage across capacitor VC=IXC=I(1/ωC)=(10/3)(1/3000(1.111 μF))=1000 V.

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