A capacitance C and an inductance L are operated at the same angular frequency.

Question

A capacitance C and an inductance L are operated at the same angular frequency. Part A At what angular frequency will they have the same reactance? Express your answer in terms of the variables C and L. Answer: w=1/sqrtLC Part B If L = 4.60 mH and C = 3.40 muF , what is the numerical value of the angular frequency in part A? (rad/s) Part C What is the reactance of each element? X_L=X_C=?       A capacitance C and an inductance L are operated at the same angular frequency. Part A At what angular frequency will they have the same reactance? Express your answer in terms of the variables C and L. Answer: w=1/sqrtLC Part B If L = 4.60 mH and C = 3.40 muF , what is the numerical value of the angular frequency in part A? (rad/s) Part C What is the reactance of each element? X_L=X_C=?       Part A At what angular frequency will they have the same reactance? Express your answer in terms of the variables C and L. Answer: w=1/sqrtLC Part B If L = 4.60 mH and C = 3.40 muF , what is the numerical value of the angular frequency in part A? (rad/s) Part C What is the reactance of each element? X_L=X_C=?       Part B If L = 4.60 mH and C = 3.40 muF , what is the numerical value of the angular frequency in part A? (rad/s) Part C What is the reactance of each element? X_L=X_C=?      

Explanation / Answer

A) Xc = 1/wC Xl = wL so, 1/wC = wL == > 1/[CL] = w^2 ==> w = 1/sqrt(LC) B) w = 7996.16 rad/s C) X_L = X_C = 36.78

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