Question

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

B.)If L = 5.10 mH and C = 3.70 μF , what is the numerical value of the angular frequency in part A?\
C.)What is the reactance of each element?

Answer 1

(B) 7279.70 rad/sec (C)
`X_L=37.1265\ ohm\ and \ X_C=37.1265\ ohm`

Step-by-step explanation:

We have given
`L=5.10mH` and
`C=3.70\mu F`

(B) The angular frequency is denoted as
`\omega` whose value is given by
`\omega =(1)/(√(LC))=\frac{1}{\sqrt{5.10* 10^(-3)* 3.70* 10^(-6)}}=7279.70\ rad/sec`

(C) The inductive reactance
`X_L=\omega L=7279.70* 5.10* 10^(-3)=37.1265\ ohm`

Capacitive reactance
`X_C=(1)/(\omega C)=(1)/(7279.70* 3.70* 10^(-6))=37.1265\ ohm`