A) Consider a series RLC circuit where R = 447 and C = 1.25 F. However, the indu

Question

A) Consider a series RLC circuit where R = 447 and C = 1.25 F. However, the inductance L of the inductor is unknown. To find its value, you decide to perform some simple measurements. You apply an ac voltage that peaks at 48.0 V and observe, using an oscilloscope, that the resonance angular frequency occurs at 15300 rad/s. What is the inductance of the inductor in millihenrys?

B) For a particular RLC series circuit, the capacitive reactance is 4.15 , the inductive reactance is 38.5 , and the maximum voltage across the 12.7- resistor is 31.5 V. What is the maximum voltage across the circuit?

Explanation / Answer

Part A:

R =447 ohms , C =1.25 uF, w =15300 rad/s

w = (1/LC)^1/2

15300 = (1/(L*1.25*10^-6))^0.5

L = 3.42 mH

Part B:

XC =4.15 ohm , XL =38.5 ohm , R = 12.7 ohm , VR =31.5 V

i = V/R = 31.5/12.7 = 2.48 A

in parallel combination current is constant

VC = 2.48*4.15 =10.29 V

VL = 2.48*38.5 =95.48 V

V = ((31.5)^2+(95.48-10.29)^2)^0.5

V =90.83 V

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