Answer to Question #309356 in Optics for Chemistry

Question

An inductor, a capacitor, and a resistor are all connected in series across an ac source.

If the resistance, inductance, and capacitance are all doubled, by what factor does each of the following quantities change? Indicate whether they increase or decrease: (a) the resonance angular frequency; (b) the inductive reactance; (c) the capacitive reactance. (d) Does the impedance double?

Answer 1

Answer

a) the resonance angular frequency is given by

$w_r=\frac{1}{\sqrt{LC}}$

When L C are double the

resonance angular frequency decrease by factor 2.

b) inductive reactance

$X_L=wL$

It becomes doubled.

c) capacitive reactance

$X_c=\frac{1}{wL}$

L becomes half.

d) the impedance

$Z=\sqrt{R^2+(X_L-X_c)^2}$

When L C R will double then it increases.