What is the value of the inductance L so that the above circuit carries the larg

Question

What is the value of the inductance L so that the above circuit carries the largest current?
Data: R = 2.31×102 , f = 1.65×103 Hz, C = 6.10×10-3 F, Vrms = 9.64×101 V.

Using the inductance found in the previous problem, what is the impedance seen by the voltage source?

You are correct. Previous Tries Consider the RLC Circuit shown in the figure. Select True False' or 'Cannot tell' for the following statements True: Energy is dissipated in the resistor but not in either the capacitor or the inductor. False: The Voltage drop across the resistor is the same as the voltage drop across the inductor at all times. True: The current through the inductor always equals the current charging/discharging the capacitor. True: The current through the inductor is the same as the current through the resistor at all times You are correct. Previous Tries What is the value of the inductance L so that the above circuit carries the largest current? Data: R 2.31 x 102 2, f 1.65x 105 Hz, C 6.10x10 F, rms 9.64 x101 V. V mit Answer Incorrect. Tries 1/20 Previous Tries Sub Using the inductance found in the previous problem, what is the impedance seen by the voltage source? Submit Answer Tries 0/20

Explanation / Answer

For the current to be largest, there must be resonance which is achieved when Xl = Xc

2pifL = 1/2 pifC

L = 1/ ( 4 pi^2 f^2) C= 1/ ( 4 x 3.14^2 x 1.65 ^2 x 10^6 x 6.10 x 10^-3) = 1/ ( 654.963 x 10^ 3) = 0.00104 mH apprx

b) Xc = 1/2pifC = 1/ ( 2x 3.14 x 1.65 x 6.10 ) = 0.0158 ohms apprx

Xl =2pifL = 2 (3.14) ( 1.65 x 10^3) ( 0.00104 x 10^-3) = 0.01077 ohms apprx

Z = sqroot ( R^2 + {Xc-Xl}^2) = sqroot ( 5.3361 x 10^ 4 + 0.000025) which is approximately equal to resistance of circuit= 2.31×102

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