In Lab 09 Investigation 1 you were asked to calculate the so-called resonance fr

Question

In Lab 09 Investigation 1 you were asked to calculate the so-called resonance frequency f_Lc. The f_LC is the input signal frequency at which the series LCR circuit's impedance Z is minimum. At f_Lc will the value of the peak current, I_max , in the circuit be a maximum or minimum? What about the value of the peak voltage, V_R,max , across the resistor? The value of I_max will reach maximum and the value of V_R,max will reach maximum as well. It happens because at the reactance of the capacitor and the inductor X_L=X_C are equal in magnitude, thus (X_L-X_C)^2=0 and therefore V_R, max / V_max=1, and Imax=Vmax/R will reach the maximum as well.The value of I_max will reach maximum but the value of V_R,max will reach minimum. It happens because at f_LC (resonance frequency) the voltage drop across capacitor, V_C,rnax, And the inductor, VL, max, reach maximum. Since the Kirchoff rule implies that V_max=VC, max+V_L,max+V_R,max, therefore V_R,max ^=V_max^_(|ar9est possible) will be minimum.The value of I_max will reach maximum but the value of V_R, max will reach minimum. It happens because at f_Lc the impedance Z is minimum and therefore the current will be maximum. However, since Ohm's law still holds for the maximal values, V_max=Z . I_max' the voltage V_R,max will be at minimum since Z is the smallest.The value of I_max will reach maximum but the value of V_R,max will be neither minimum nor maximum. It happens because at f_LC the impedance Z is minimum and therefore the current will be maximum. However, since Ohm's law still holds for the maximal values, V_max=Z . I_max, voltage V_R,max will not necessarily be at maximum at the same time because current is maximum and Z is minimum so we can not tell.

Explanation / Answer

according to0 kirchoff's laws

Vmax = Vmax,R +vmax,L + Vmax,C

impedence becomes Z = R at the resonance

Imax = Vmax/Z

if Z becomes minimum then Imax is maximum value

vmax,L = Imax*XL and Vmax,C = Xc*Imax

here XL = XC

then Vmax,L = Vmax,C becomes same and maximum

then Vmax,R = Vmax-(largest possible) will be minimum

So finally the answer is

The value of Imax will reach but the value of VR,max will reach minimum.it happens because at fLC the voltage drop across capacitor VC,max and the inductor VL,max reach maximum.Since the kirchoff's rule implies that Vmax = VC,max + VL,max +VR,max therefore VR,max = Vmax - (largest possible) will be minimum

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