An ac series circuit contains a 20 ohm resistor, a capacitor of 0.75 micro farad, and an inductor of 120 mH. What frequency should be used to create a resonance condition

530.5 Hz

Explanation:

Given :

C=0.75 micro

L=120 mH

Reactance capacitor can be determined by

=

where c =capacitor

=

Reactance inductor can be determined by

As they are in series so ,

On solving these value we get

As we know that

f = =

530.5 Hz

f=ma newton

f=100x2.5=250n

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .