Question

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

a. At what angular frequency will they have the same reactance?

b. If L=5.00mH and C=3.50 μF,what is the numerical value of the angular frequency in part (a), and what is the reactance of each element?

Answer 1

Answer:

a) ω = √(1/CL

b)7559.29 rad/s

   37.796 Ω

Explanation:

a) Reactance of capacitor (Xc) = 1/(Cω)

Reactance of Inductor (XL) = Lω

when both have the same ω and reactance

Lω = 1/Cω

ω² CL =1

ω = √(1/CL)

b) ω = √(1/CL)

        = $\sqrt{\frac{1}{5*10^{-3} *3.50*10^{-6} }}$

        = 7559.29 rad/s

Reactance of capacitor (Xc) =Reactance of Inductor (XL)

                                             = Lω

                                              = 37.796 Ω