Acapacitance c and an inductance l are operated at the same angular frequency.

a) at what angular frequency will they have the same reactance? express your answer in terms of the variables c and l.
b) if l = 5.30mh and c = 3.40 μf , what is the numerical value of the angular frequency in part a?
c) what is the reactance of each element?

A)

The magnitude of the capacitive reactance is given by

where

is the angular frequency

C is the capacitance

While the magnitude of the inductive capacitance is given by

where L is the inductance.

Since we want the two reactances to be equal, we have

So we find

B) 7449 rad/s

In this case, we have

is the inductance

is the capacitance

Therefore, substituting in the formula for the angular frequency, we find

C)

Now we can us the formulas of the reactances written in part A). We have:

- Capacitive reactance:

- Inductive reactance:

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form