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Bandwidth Formula RLC circuit
By BYJU'S Exam Prep
Updated on: September 25th, 2023
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
Table of content
Answer: 30 ohms, 1000 V
The bandwidth formula for the series rlc circuit is B.W=R/L.
Solution:
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
ωL=1/ωC
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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