Bandwidth Formula RLC circuit

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 ω_r=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 X_L=X_C

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 V_C=IX_C=I(1/ωC)=(10/3)(1/3000(1.111 μF))=1000 V.

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