A 33.0-mH inductor has a reactance of 2.20 kΩ.
(a) What is the frequency of the ac current that passes through the inductor?
(b) What is the capacitance of a capacitor that has the same reactance at this frequency?
(c) The frequency is tripled, so that the reactances of the inductor and capacitor are no longer equal. What is the new reactance of the inductor?
(d) What is the new reactance of the capacitor?
See previous post.
To solve these problems, we need to use the following formulas:
(a) Frequency of AC current passing through an inductor: f = 1 / (2π√(LC))
(b) Capacitance of a capacitor with the same reactance: C = 1 / (2πfX)
(c) New reactance of the inductor when the frequency is tripled: X_new = X_initial / 3
(d) New reactance of the capacitor when the frequency is tripled: X_new = X_initial * 3
Now let's solve each part step by step:
(a) To find the frequency of the AC current passing through the inductor, we can rearrange the formula:
f = 1 / (2π√(LC))
Given:
L = 33.0 mH = 33.0 x 10^-3 H
X = 2.20 kΩ = 2.20 x 10^3 Ω
Substituting the values into the formula:
f = 1 / (2π√(33.0 x 10^-3 H x 2.20 x 10^3 Ω))
To find the answer, you'll need a calculator to perform the calculations.
(b) To find the capacitance of a capacitor that has the same reactance at this frequency, we can use the formula:
C = 1 / (2πfX)
Given:
f = the frequency from part (a)
X = the reactance from part (a)
Substituting the values into the formula:
C = 1 / (2π x frequency x reactance)
To find the answer, use the values calculated in part (a) and the reactance given.
(c) To find the new reactance of the inductor when the frequency is tripled:
X_new = X_initial / 3
Given:
X_initial = the reactance from part (a)
Substituting the values into the formula:
X_new = reactance / 3
To find the answer, divide the reactance from part (a) by 3.
(d) To find the new reactance of the capacitor when the frequency is tripled:
X_new = X_initial * 3
Given:
X_initial = the reactance from part (a)
Substituting the values into the formula:
X_new = reactance * 3
To find the answer, multiply the reactance from part (a) by 3.