at 3.68100017 kHz the reactance in a circuit of a 9 uF capacitor and an inductor are equal in magnitude. what is the value of the inductor?

Xl = Xc = 1/6.28FC.

Xl = 1/(6.28*3681*9*10^-6) = 4.807 Ohms
Xl = 6.28FL. = 4.807.
L = 4.807 / (6.28*3681) = 0.00021 h. =0.21 mH.

My answer don't agree with any of the
given answers.

Henry's solution is in correct spelling of the given answers :)

To find the value of the inductor, we can use the formula for reactance in a circuit containing a capacitor and an inductor:

Xc = 1 / (2πfC)
Xl = 2πfL

Where:
Xc is the reactance of the capacitor
Xl is the reactance of the inductor
f is the frequency of the circuit
C is the capacitance
L is the inductance

Given:
frequency, f = 3.68100017 kHz
capacitance, C = 9 uF (microfarads)

We are looking for the value of the inductance, L, when Xc and Xl have equal magnitude.

At the frequency where Xc = Xl:
1 / (2πfC) = 2πfL

Simplifying the equation further:
1 / (2πfC) = 2πfL
1 = (2πfL)^2 * (2πfC)
1 = L^2 * (4π^2f^2) * C

Substituting the given values:
1 = L^2 * (4π^2 * (3.68100017 * 10^3)^2) * (9 * 10^(-6))

Solving for L:
L^2 = 1 / ((4π^2 * (3.68100017 * 10^3)^2) * (9 * 10^(-6)))
L^2 = 1 / (4.24960016176 * 10^9 * 9 * 10^(-6))
L^2 = 1 / 38.246401454784
L^2 ≈ 0.0261799

Taking the square root of both sides:
L ≈ √0.0261799
L ≈ 0.1616944

Therefore, the value of the inductor is approximately 0.1616944 H.

None of the answer choices provided match the calculated value, so there might be a mistake in the given options or in the question itself.

To determine the value of the inductor, we need to equate the reactance of the capacitor and the inductor in magnitude. The reactance of a capacitor (Xc) is given by the formula:

Xc = 1 / (2πfC),

where f is the frequency in Hertz and C is the capacitance in Farads.

Similarly, the reactance of an inductor (XL) is given by the formula:

XL = 2πfL,

where f is the frequency in Hertz and L is the inductance in Henrys.

In this case, we are given the frequency (3.68100017 kHz) and the capacitance (9 uF) and we need to find the inductance.

Start by converting the frequency to Hertz:
3.68100017 kHz = 3,681 Hz

Next, we'll substitute the values into the reactance formulas:

Xc = 1 / (2π * 3681 * (9 * 10^-6)),

XL = 2π * 3681 * L.

Equate the two reactances:

1 / (2π * 3681 * (9 * 10^-6)) = 2π * 3681 * L.

To solve for L, perform the following calculations:

1 / (2π * 3681 * (9 * 10^-6)) = 2π * 3681 * L.

0.00000054724053 = 2.28502618 * L.

L ≈ 0.00000054724053 / 2.28502618.

L ≈ 2.39187 * 10^-7.

The value of the inductor is approximately 0.000000239187 H, which is equivalent to 0.239187 µH.

Therefore, the correct answer is option (c) .000021 µH.