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quellcrist
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1. An RLC series circuit has C= 4.8mF, L=0.520H, and source voltage amplitude V= 56.0V. The source is operated at the resonance frequency of the circuit. If the voltage across the capacitor has amplitude 80.0V, what is the vaule of R for the resistor?
2. ##I = (ΔVc)/(Xc)##,
##Xc= (1)/(ωc) ##,
## ω= (1)/(sqrt(LC)) ##
resonance frequency = ## (1)/(sqrt(LC)) = 20Hz##
##Xc= 10.4 ##
## Ic = IL = Ir ## in an RLC series circuit
therefore ## I= 80V/10.4 = 7.7##
At resonance frequency ##X=R##
Z is at a minimum
R is at a minimum, VL and VC cancel each other other becoming 0,
##Z= sqrt((R)^2+(XL-Xc)^2)##
##Vr=sqrt((ΔVtotal)^2-(ΔVL-ΔVc)^2)##
3. I know this question shouldn't be that hard but I have hit a mental block and cannot proceed. I know how to calculate impedance but the value of R isn't given. My question is "How do I calculate impedance when R is not given?" I know the RLC series circuit becomes purely resistive at resonance and that Z is at a minimum and Z=R. Thanks!
2. ##I = (ΔVc)/(Xc)##,
##Xc= (1)/(ωc) ##,
## ω= (1)/(sqrt(LC)) ##
resonance frequency = ## (1)/(sqrt(LC)) = 20Hz##
##Xc= 10.4 ##
## Ic = IL = Ir ## in an RLC series circuit
therefore ## I= 80V/10.4 = 7.7##
At resonance frequency ##X=R##
Z is at a minimum
R is at a minimum, VL and VC cancel each other other becoming 0,
##Z= sqrt((R)^2+(XL-Xc)^2)##
##Vr=sqrt((ΔVtotal)^2-(ΔVL-ΔVc)^2)##
3. I know this question shouldn't be that hard but I have hit a mental block and cannot proceed. I know how to calculate impedance but the value of R isn't given. My question is "How do I calculate impedance when R is not given?" I know the RLC series circuit becomes purely resistive at resonance and that Z is at a minimum and Z=R. Thanks!