Question

Consider a driven RLC series AC circuit. At frequency f1 the capacitive reactance is twice the inductive reactance. Determine frequency f2 as a function of f1 so that the inductive reactance is twice the capacitive reactance.

Select one:

a.

f2=f1/sqrt(2)

b.

f2= sqrt(2)f1

c.

f2= 2f1

d.

f2=f1/2

Answer 1

c. f2= 2f1

Let C is the capacitance of capacitor and L is the inductance of inductor.

At frequency f1 the capacitive reactance is twice the inductive reactance,

XC1 = 2*XL1

1/(2*pi*f1*C) = 2*2*pi*f1*L

f1^2 = 1/(8*pi^2*L*C) -------(1)

At frequency f2 the inductive reactance is twice the capacitive reactance,

XL2 = 2*XC1

2*pi*f2*L = 2*1/(2*pi*f2*C)

f2^2 = 1/(2*pi^2*L*C) -----(2)

take equation(2)/equation(1)

f2^2/f1^2 = ( 1/(2*pi^2*L*C))/(1/(8*pi^2*L*C))

f2^2/f1^2 = 4

f2/f1 = sqrt(4)

f2/f1 = 2

f2 = 2*f1